LaVeyan Satanism I am Satan. I am my own god and believe in myself. I believe in my own abilities and power and don't need any spiritual being helping me.
Theistic Satanism Satan is a real entity. I belive in him as Christains do in their Jesus. I am loyal to Satan and will take every challange he gives me. *Some of us believe only in Satan while others believe in both our Satan and the Christain God.
Devil Worshippers I worship everything I find to be evil. I will sacrifice anything or indulge in crimes for Satan, who I belive is the Devil and symbol of evil himself.
Luciferianism I believe in Lucifer. Lucifer is an enlightened and spiritual being, more peacful than Satan. I believe that the world is devided into light and darkness.
Demonolators I believe in and honor actual demons rather than Satan. Thanks to rituals or meditation I can contact demons and ask for their assistance when I need it.
Duotheism I believe that Satan isn't a god, but rather the bible based being who has rebelled against the Creator and forcefully tried to take his throne.
Ecletic Satanism I am none of the above. I have different beliefs from two or more religions and combine them. I have my own non-specific religion.
There might be a few other, more specific, types of Satanism I haven't covered. I also might have made mistakes on these so feel free to correct or add on! I did not include Satin Satanism since I couldn't find much information about it, and from what I'm hearing it isn't really a form of Satanism.