There are many kinds of Satansims. The ones I’ve studied are LaVeyan, Theistic/Spiritual, Devil worshipers, Luciferianism, and pseudo Satanism.
LaVeyan Satanism
This is atheistic. They see Satan as a symbol. In the torah, "Satan" means the adversary. LaVeyan Satanism challenges the status quo. They do not believe Satan is an actual being. He is a symbol to them that represents different things.
1. Satan represents indulgence instead of abstinence!
2. Satan represents vital existence instead of spiritual pipe dreams!
3. Satan represents undefiled wisdom instead of hypocritical self-deceit!
4. Satan represents kindness to those who deserve it instead of love wasted on ingrates!
5. Satan represents vengeance instead of turning the other cheek!
6. Satan represents responsibility to the responsible instead of concern for psychic vampires!
7. Satan represents man as just another animal, sometimes better, more often worse than those that walk on all-fours, who, because of his “divine spiritual and intellectual development,” has become the most vicious animal of all!
8. Satan represents all of the so-called sins, as they all lead to physical, mental, or emotional gratification!
9. Satan has been the best friend the Church has ever had, as He has kept it in business all these years!
The basic philosophies LaVey came up with is very good. But he was a power hungry, sell out fraud. Most of his 'history' about Satan is fake. Baphomet was NOT worshiped as Satan, the yezids do NOT worship Satan, and the Al-Jiwah is NOT the black book of Satan. Decent philosophy, scam religion.
The religion has a lot of hate in it. In The Satanic Bible, the first chapter (the book of Satan), it says “I gaze into the glassy eye of your fearsome Jehovah, and pluck him by the beard. I uplift a broad axe and split open his worm eaten skull.” Now this is symbolic, like the whole religion, but still very violent. Also, the religion promotes use of black magick as if there is nothing wrong with it.
Theistic/Spiritual Satanism is what Joy of Satan is but they are a bad example. They encourage Nazism and a self mutilation ritual to give your soul to Satan. Once again, most of their 'history' is false to make you believe more. In this case, the deity/deities being worshiped is not the Christian Satan. They believe the god is the true creator god. In a lot of cases, the belief is that Satan is some kind of extraterrestrial being. Most Theistic/Spiritual Satanists are polytheistic and believe. It is usually rare that they believe in the Christian god at all. When they do, They believe that the Christian god stole Satan’s credit for creating the world. They use god’s horrible deeds in the bible to prove he is not all loving like religions claim. Other Theistic/Spiritual Satanist have their own unique beliefs. Most belief, whatever god they think the creator god is was perverted into Satan to hide the god’s identity. They call him Satan because people are not worthy to know his identity. In this case, many people could be considered Theistic/Spiritual Satanists.
Devil Worshipers are extremely rare. They worship the Christian Satan. They believe god is ALL forgiving and Satan is ruler of this world. So, they feel they have to please Satan. This can be done through self mutilation, vandalism, and in extreme rare cases even animal sacrifice. Nothing like Satanic Ritual Abuse though. It is not like they are holding kidnapped women hostage to have babies to sacrifice. The Satanic Ritual Abuse was proved false. If they do not please Satan they fear they will go to hell.
Luciferianism is the Satanism I know least about. They believe Lucifer is the bearer of light and can bring them infinite knowledge. They believe in the positive aspects of Satan. There are several groups of Luciferians (I think that is what you would call them.)
Last, Pseudo Satanists are just posers. They have really no religious connection to any kind of Satanism. They just get off on trying to scare people with carving pentagrams into churches and stuff.
Last I would like to state that, as far as I know, there has never been a confirmed case of a human Satanic ritual murder in the United States.