I have noticed people try and differentiate between the CoS, and other groups who claim to be Satanism and yet worship a deity, wouldn't Luciferianism be a more appropriate term for them? Just so that people understand? I am sure there are more divides on this as well, but isn't that basically what these other groups are?

The most appropriate term is Heretical Christian. That really is all they are. Same idiotic mythology, same sort of idiot embracing it.

Please read Church of Satan FAQ: 3. Fundamental Beliefs, E. What is “Theistic Satanism?