@se7en @galena@blob.cat @ikocevski LaVeyan Satanism officially considers the first category you mentioned, worship of Satan as an actual, real deity, to be "devil worship" and not "Satanism". LaVeyan Satanists are very, very careful to avoid referring to it as Satanism, to avoid getting themselves mixed in with devil worshiping groups and accused of being associated with crimes they're uninvolved with. To them, LaVey invented the concept of "Satanism" as a religion, and only religions derived from LaVeyan Satanism can be called "Satanism". I try to avoid referring to devil worship as Satanism too, though I'll occasionally call it "Theistic Satanism" when referring to more established groups that believe in those kinds of things (eg Temple of Set) because they are an actual offshoot of LaVeyan Satanism, despite believing "Satan" (or Set, specifically) is real.
Satanists have a very long history of being grouped in with insane cultists, devil-worshipers who commit heinous crimes, and other such fringe groups, and I'd rather not grant any legitimacy whatsoever to those claims. I'm sure you've seen how easy it is for a group to be co-opted and corrupted if it doesn't constantly police itself and who it accepts and who it rejects when they use its name. When I use the term "Satanist", I am referring primarily to LaVeyan Satanism and associated religions, because I don't consider devil worshipers to be Satanists.