IMO, theistic Satanists seem to be people who replace the word "God" with the word "Satan". But they'll never say this. Most of them will just say that Satan is the lesser of two evils compared to God. They might use references such as the 'genocidal' flood in Abrahamic texts to support this.
Atheistic Satanists believe in Satan as an archetype, who respresents traits which should be desired. Like living your life to the fullest, enjoying life, doing whatever you want if you enjoy it and it harms no one, only respecting your own authority, rebelling... etcetera.
Please correct me if I'm wrong.