The single most common error about modern Satanism is that its adherents believe in the devil. The two organisations that account for most Satanists in the world do not. LaVeyan Satanism, set out in Anton LaVey's Satanic Bible of 1969, is atheistic and materialist. Satan is a symbol: of pride, of appetite, of the human being as an animal rather than a fallen angel, and of refusal to accept authority that cannot justify itself. LaVey was explicit that anyone worshipping a literal devil had simply adopted the Christian cosmology and taken the losing side of it. The Satanic Temple is atheistic on the same terms, invoking the literary Satan of Milton and the Romantics as the eternal rebel against tyranny.
What follows from this is that Satanic ritual is not directed at anyone. Ceremony in the LaVeyan system is described frankly as psychodrama: theatre using blasphemous imagery to produce an emotional effect on the participants, on the reasoning that ritual works on the human nervous system whether or not any spirit is listening. The Satanic Temple has adapted the same logic to political ends, staging rituals whose purpose is to assert legal parity with religions that expect deference.
Where the two differ sharply is ethics. The Church of Satan teaches indulgence rather than abstinence, vengeance rather than turning the other cheek, and responsibility only to the responsible; it is elitist by design and hostile to egalitarianism. The Satanic Temple's seven tenets run in a different direction: act with compassion and empathy, struggle for justice, hold one's own body inviolable, respect the freedoms of others including the freedom to offend, revise belief in the light of evidence, make amends for wrongs, and read any written word by its spirit rather than its letter. There is no supernatural content in either list.
Theistic Satanism does exist. Some groups treat Satan as a genuine being, whether as the adversary of the biblical god or, in the Temple of Set, as an Egyptian deity misnamed by later tradition. Others operate outside any organisation at all. But there is no theistic body of a size comparable to the two atheistic ones, and treating theistic Satanism as the normal case reverses the actual proportions.