In their attempts to dissociate themselves from Satanism, Wiccans have tended to distort their own history. Wicca and Satanism are indeed very distinct religious categories. But there are some intimate historical ties between the two, as even some Wiccan scholars are finally starting to admit. See, for example, Aidan Kelly's book Crafting the Art of Magic (pp.21-22, 25-26, and 176).
Wicca is not "the Old Religion", though it does draw inspiration from various old religions. Wicca as we now know it is derived from 19th-century occult philosophy -- including literary Satanic philosophy, among others -- projected onto a non-Christian Goddess and God, plus some de-Christianized Golden Dawn style ceremonial magick, plus assorted turn-of-the-century British folklore, more recently re-shaped by neo-Pagan scholarship and by modern feminist and ecological concerns. At least several different sides of Wicca's convoluted family tree can be traced to 19th-century literary Satanism, some forms of which had more in common with present-day Wicca than with present-day Satanism.
The prime example of literary Satanism that strongly influenced Wicca, especially feminist Wicca, is the book La Sorciere by the 19th-century French historian Jules Michelet (published in English by Citadel Press under the title Satanism and Witchcraft). Michelet's ideas, as paraphrased by feminist writers such as Barbara Ehrenreich and Deirdre English in their booklet Witches, Midwives, and Nurses: A History of Women Healers (Feminist Press, 1973), have played an important role today's women's health movement. (At least Ehrenreich and English were honest enough to list Michelet in their bibliography.) See especially Michelet's introduction. Michelet was, as far as I know, the literary origin of today's feminist image of the Witch as a healer. Among other things, he theorized that the witchhunts were used by the emerging male medical profession to wipe out their peasant female competition.
According to Jeffrey B. Russell in A History of Witchcraft, pre-feminist classical Wicca also drew lots of inspiration indirectly from Michelet. Michelet was a major source of inspiration to Margaret Murray, Charles G. Leland, and Sir James Frazer, whom most knowledgeable Wiccans do recognize as influential. (Russell points this out, yet neglects to inform the reader that Michelet's book is full of passionate, sympathetic depictions of Satan as well as of the medieval witches. Russell too perpetuates the false counter-myth that Wicca Has Nothing To Do With Satanism.)
I'll leave it to folks more scholarly than myself to debate just how indebted Murray and Leland were to Michelet. In any case, the Italian witch mythology Leland presented in Aradia: Gospel of the Witches (originally published 1899), one of Wicca's major sources, contains some diabolical-witchcraft elements of its own. The very first paragraph reads:
Wiccans usually argue that "Lucifer" is not the Christian Devil but is just "the god of the Sun and of the Moon". (I too distinguish between Satan and Lucifer, as do many occultists.) Yet the statement that Lucifer was "driven from Paradise" for his "pride" is clearly a reference to Christianity's Devil myth. Aradia contains a mix of mythologies.
Wiccans are correct to say that their Horned God is not Satan. But it isn't historically true that the Christian image of Satan is a re-interpretation of the Wiccan God. On the contrary, the modern Wiccan concept of the Horned God has its literary origin in a Paganized re-interpretation of medieval Christian Devil imagery (as in Margaret Murray's and earlier writings). It's true that medieval Christian Devil imagery, in turn, incorporates distorted versions of many ancient Gods (not all of whom were Horned, e.g. the trident comes from Poseidon/Neptune). But the Wiccan image of its Horned God is not a direct continuation of any ancient religion, and at least one key aspect does come from no source other than the medieval Christian Devil concept as manifest in the witchhunts. The idea of a Horned God associated specifically with witchcraft is derived from the Christian witchhunts, and from no previous source. In pre-Christian European religion, there were Goddesses associated with witchcraft, e.g. Hecate; but Pan and other horned male Gods were not associated with witchcraft, as far as I know. Much of Wicca's self-image is based on the Paganized re-interpretation of alleged Devil-worship, rather than on actual ancient religion. Much of Wicca's terminology and imagery, e.g. the words "witch", "coven", and "sabbat", are used because of the Wiccan myth that Wicca is the survival of an underground medieval religion that was the target of the witchhunts. (Regardless of the linguistic origin of the words themselves, this constellation of terms comes from the witchhunts.) The related idea that modern Wiccans too are in continual danger of being confused with Satanists is at least partly a self-fulfilling prophecy. Far fewer people would confuse modern Wicca with Satanism if Wicca didn't use so many witchhunt-derived words and other trappings popularly associated with diabolical witchcraft.
My point here is not that Wiccans shouldn't use the words "witch", "coven", and "sabbat". My point is that if they do use these and other diabolical-witchcraft trappings, they should accept responsibility for the consequences. For example, when explaining that Wicca Is Not Satanism, they should acknowledge the main real reason for the confusion: that modern Wiccans have chosen to identify with the victims of European witchhunts and have chosen their terminology accordingly. Wiccans certainly should not blame Satanists for Wicca's own public-relations difficulties, as some Wiccans do. It also bothers me when Wiccans, in an attempt to distance themselves from Satanism, perpetuate popular misconceptions about Satanism, e.g. saying "We're not Satanists!" in a tone which implies you think Satanists are monsters, or saying "We're not Satanists!" in the same breath as saying "We don't sacrifice babies." (The latter point can be made separately and is an obvious corollary of the Wiccan Rede and/or the Threefold Law.)
Back to Wicca's history. Besides Murray, Leland, and other writers on witchcraft, another of Wicca's main sources is Aleister Crowley. Many knowledgeable Wiccans (e.g. the Farrars and Doreen Valiente) do realize that Gardner's rituals were heavily based on Crowley's rituals, though they tend to overstate the "Crowley was not a Satanist" disclaimer.
Crowley was not a Satanist per se, but he definitely was into Satanic symbolism, in addition to the zillion other things he was into. In some defensive neo-Pagan writings (e.g. the Church of All Worlds booklet "Witchcraft, Satanism, and Occult Crime: Who's Who and What's What"), it is claimed that Crowley was neither a Satanist nor a Pagan but was just into Judaeo-Christian ceremonial magick. In fact, Crowley was very eclectic. Even Golden Dawn ceremonial magick included not only Qabalah and the medieval Christian grimoires, but also Egyptian deities, Greek deities, and Yoga. Crowley emphasized the Egyptian elements, downplayed the Christian elements, and added plenty of other things to the mix, including Satanic imagery galore (such as his invocation of Satan in Liber Samekh, not to mention his constant references to himself as "the Beast 666"). Some will insist that Crowley's Satanic symbolism was merely a joke; but Crowley's attitudes were well within the 19th-century Satanic literary tradition. (In most of the more sophisticated forms of Satanism, the name "Satan" is understood in an ironic sense.) Others will explain that most of Crowley's Satanic symbolism can be re-interpreted in Pagan terms, but this too is true of many forms of Satanism.
There's also a possibility that Wicca borrowed ideas from writings about actual Satanists living in the late-19th or early-20th century. In Crafting the Art of Magic, Aidan Kelly says Gerald Gardner drew key concepts from the description of Ozark folk witchcraft, including folk Satanism, in the 1947 book Ozark Superstition by Vance Randolph. I'll admit that Kelly's conclusions have been challenged by other historically-knowledgeable Wiccans.
Of course, if Gardner was influenced by Randolph's account, Gardner would probably have assumed that the Satanic folk witches were "really" Pagans whom Randolph misrepresented as Satanists. But Gardner's assumption wouldn't necessarily have been correct. An unlettered folk-witch would be far more likely to be either (1) a Satanist or (2) a devout though unorthodox Christian than to have preserved an ancient Pagan religion intact. Various Pagan customs have certainly survived, but this is very different from the intact survival of a Pagan religion, for which there is very little evidence. (For a critique of alleged evidence for Pagan survival, see A Razor for a Goat by Elliot Rose. Regarding a possible medieval witch-cult very different from what Murray hypothesized, see The Night Battles by Carlo Ginzburg. Regarding contemporary hereditary witches, many of whom are Christian, see Bluenose Magic by Helen Creighton. For an example of a decidedly non-Pagan grimoire that is very popular among European folk witches today, see The Sixth and Seventh Books of Moses, available in some botanicas.)
Some forms of Wicca may have been influenced by Satanists more directly than via Murray, Leland, Crowley, Ehrenreich/English, and possibly Randolph. Two possible examples:
(1) Historically-knowledgeable Wiccans have debated what role, if any, was played in the development of modern Wiccan by a 19th-century English farm laborer named George Pickingill who was reputed to be a witch. Aidan Kelly, who does not believe Pickingill contributed anything to Wicca, describes Pickingill as "a garden-variety folk-magic witch and a home-grown Satanist." The assertion that Pickingill did play a major role was originally made by "Lugh" in a newsletter called The Wiccan in 1974. "Lugh", who claimed to be a hereditary witch, described Pickingill as "the world's greatest living authority on Witchcraft, Satanism, and Black Magic" (quoted by Doreen Valiente in Rebirth of Witchcraft).
(2) Starhawk was initiated by Victor Anderson, who once belonged to a coven whose form of witchcraft included a form of "literature-based Satanism" (or at least a religion closely akin to "literature-based Satanism"); or so says Kelly, based on research by Valerie Voigt.
Whether or not Kelly is correct about Victor Anderson, and whether or not Pickingill had anything to do with Wicca, it shouldn't be considered unlikely that some traditions of Wicca originated as forms of Satanism and then gradually grew away from Satanism. To this day, there are occultists who start out as Satanists and eventually become Wiccans or other types of neo-Pagans. It would be very odd if such people's understanding of Wicca was not at all influenced by their previous experience with Satanism.
Theistic forms of Satanism have a natural tendency to give birth to new, non-Satanic religions. If you reject Christian theology (as nearly all intelligent Satanists do), but if you nonetheless venerate Satan as a real being or force (not just a symbol as in LaVey Satanism), then the question inevitably arises: Who and what is "Satan"? Different forms of Satanism have different answers to this question. One of the easier answers is to re-interpret Satan as a pre-Christian deity, usually either Set or Pan. However, once you equate Satan with a specific ancient deity, you have taken the first step away from Satanism. You are no longer venerating Satan per se; you are now venerating a Pagan deity with Satanic overtones. And then, once you develop your Paganized belief system further, the Satanic overtones will eventually seem less and less important. Such has apparently been the case with the Temple of Set, an offshoot of LaVey's Church of Satan. (Setians disagree on whether to call themselves "Satanists".) It seems not at all unlikely that some forms of Wicca, with all its diabolical-witchcraft trappings, would have a similar origin. A group of theistic Satanists who equated Satan with Pan, as some Satanists do, would very likely tend to evolve in a Wicca-like direction.
More about Wicca's diabolical-witchcraft trappings. Wicca's self-image is based on the records of witchhunts, re-interpreting the alleged activities of accused diabolical witches as the worship of a Pagan "Horned God". Wicca thus makes a new use of the same source material that Satanists have been using for centuries.
An interesting question is: Why reconstruct an "Old Religion" this way, rather than just going back to the records of actual old religions? Other forms of neo-Paganism, e.g. Asatru and neo-Druidism, which do base themselves more on what's known about actual ancient religions, are far less likely than Wicca to be confused with Satanism by outsiders. Why do Wiccans insist on using words like "witch" and "coven" when they could easily use other, more respectable-sounding words?
Despite Wicca's diabolical-witchcraft trappings, or perhaps partly because of those trappings, Wicca has more popular appeal than any other form of neo-Paganism. Certainly Wicca's hot-button terminology has helped Wicca get lots more publicity than it otherwise could. Wiccan spokespeople sometimes bemoan the fact that newspapers interview them only at Halloween, but most small religious sects don't get nearly so much free publicity at any time of the year, not even on Halloween. And, judging by the way some Wiccans keep repeating "We're Not Satanists!" far more often than they actually get accused of being Satanists, it seems logical to suspect that at least some of them are using words and images popularly associated with Satanism as a way to attract attention, and/or because they themselves enjoy feeling naughty. (I've actually heard some Wiccans say that if the word "witch" ever became too respectable, it would lose some of its power.) Modern Satanists have long felt that the basis of Wicca's appeal lies in the paradoxical (some would say hypocritical) combination of Wicca's Satanic connotations and the denial of same. Thus, Satanists tend to regard Wicca as a ripoff of Satanism.
I personally don't regard Wicca as a ripoff. In my opinion, Wiccans' use of witchhunt-derived trappings is neither more nor less legitimate than the use of those same trappings by Satanists. And Wicca, as a religion, does have much more substance to it than just its deliberately-adopted superficial resemblances to diabolical witchcraft.
But I'm very irritated by those endless "Wicca Has Nothing To Do With Satanism!" disclaimers. I wouldn't mind if Wiccans merely said that Wicca is not Satanism (at least if they said it without repeating it unnecessarily). It's true that Wicca is not Satanism, but it isn't historically true that Wicca "has nothing to do with" Satanism. Nor is it true that Wicca has nothing in common with Satanism. Some forms of Wicca and neo-Paganism have a lot in common with (some forms of) Satanism.
Oddly enough, of the many Wicca-based forms of neo-Paganism, one of the most "Satanic" (in terms of 19th-century literary Satanism) is feminist Goddess religion, despite its frequent omission of even the "Horned God". See, for example, some of Mary Daly's writings. When it comes to inverting and parodying Christian symbolism, Daly's wordplay does it better than an old-fashioned Black Mass. Daly also reclaims and venerates almost every demonized female category conceivable, from Furies to Hags. And let's not forget the many feminists who venerate Lilith, a Jewish folkloric near-equivalent of the Christian Satan. Lilith never made it to the status of a full-fledged anti-god, but otherwise her myth is almost identical to the Christian Satan myth: banished for her pride, she became a dreaded demon and was even blamed for people's sins, especially sexual ones. To be fair, I should mention that not all feminist Goddess-worshippers are into either Mary Daly's writings or the veneration of Lilith. But the feminist counterculture, because it is a counterculture, tends generally to include an extra dose of demon-reclamation beyond what is found in classical Wicca, e.g. magazine titles like Sinister Wisdom. All these parallels to Satanism reflect the quintessentially Satanic central theme of some forms of feminist Goddess religion: self-liberation from a socially-imposed mainstream "spiritual" order -- even though Goddess religion is in other ways quite "un-Satanic" by the standards of most modern Satanists.
One of the earliest feminist writers on religion had a much friendlier attitude toward Satanism than is common today. As far as I know, the very first feminist writer on witchcraft and Goddess religion was 19th-century womens's suffrage leader Matilda Joslyn Gage. Her book Woman, Church, and State contains an enthusiastic depiction of a medieval peasant Black Mass, based on Michelet's account. I hope today's Wiccans and feminist Goddess-worshippers will stop fearing to recognize that, just as Christianity borrowed heavily from Greek mystery religion yet is a very different religion from the Greek mysteries, so too Wicca and feminist Goddess religion have drawn lots of inspiration from Satanism, though they are very different religions. Kelly's honesty is refreshing. If today's Satanists are sometimes nasty to Wiccans, well, how would you react to a bunch of people who went out of their way to deny their own roots, just so they could disown you?
What's especially annoying is the way many Wiccans claim the word "Witchcraft" as a name for their own religion, defining not only "Wicca" but also "Witchcraft" as a religion distinct from Satanism. Excuse me, but witchcraft is not a religion. There are witches all over the world, in many different cultures. They don't all belong to one religion. A witch can be any religion. One of my great-grandfathers was a "water witch" who told people where to dig wells. He was a devout Christian. If a Christian can be a witch, then so can a Satanist. There have been both Christians and Satanists calling themselves witches long before today's Wiccans came along. (See Randolph's and Creighton's books, for example.) So I really wish Wiccans would stop using the word "witchcraft" as a name for their own specific religion. I don't object to Wiccans calling themselves witches, but I do object to the idea that all true witches are Wiccan (or at least Pagan) and that, therefore, Satanists can't be witches.
Wiccans are welcome to call their specific religion "Wicca", an archaic word that they themselves resurrected. Another good name for their specific religion is "Neo-Pagan Witchcraft", a phrase suggesting that their religion is a subcategory of witchcraft, not witchcraft as a whole. Thus, it's accurate to say, "Neo-Pagan Witchcraft is not Satanism", whereas it's misleading to say, "witchcraft (in general) is not Satanism".
It would also be nice if Wiccans would stop making inaccurate pronouncements on what Satanism is, such as, "Satanism is a form of Christianity" or "To be a Satanist, you must believe in the Christian God".