As far as I see this discussion going it mainly focus on the "occult" part.
Atheistic / LaVeyan Satanism -
This uses satanic symbolism for shock value / power trough fear. It may focus on Satan as an adversarial force against society and adjust their own image accordingly. It may see carnal pleasure as the ultimate goal and therefore be hedonistic. An individual may just like the mythology and symbols, it really varies. To be honest, this is hardly even satanism, more flashy imagery than occultism.
I harshly disagree with this one. Puting Lavey and the general atheistic satanism in one pot is a a really dull action. Laveys picture was more a cry against old fashioned and traditional christian structures and thinking of his time, it simply was his own personal rebellion to cry out to this one God "FUCK YOU!".
On the other hand considering the book of leaviathan (correct me if I confise the chapter) Laveys work goes a little bit into the occult direction.
Atheistic satanism generally spoken is mostly very far away from this. As you said it is mostly work with flashy pictures and thoughts. This one is of course also not a conform unit and also has its variuos directions, but it makes up the majority of the people calling themselves satanists as far as I recall. It is about those pictures and images and thoughts, going pout on its own as a kind of subculture and philosophy, far away from occultism in most cases.
I would consider it more like a kin to the punk movement from the way it evolved.
Magickal oriented satanism is a small part in the scene, and the word "satan" in the name of this movement is missleading for many people implicating that the devil himself must be involved which is definitly not the case. It may have been in the origins, as this crazy lavey turned away from christianity and took the next thing he saw as opposite to god into the name of his new way of thinking, but the devil as deity is not involved into satanism as way of thinking today. It is a synonym for the pictures, images and thoughts I spoke of.
Devil worship on the other hand is not necessarily involved in satanistic circles and their thinking. It simply is about worshiping this deity called "devil" but even there it is difficult because the interpretations what the devil really is, they differ a lot, varying from Lucifer to Satan to even fusions of several beings (involving Belial, leviathan, etc). Some chaotic approaches met the devil worshipping ways and created interesting practices like "The Current of Set" by Frater Eremor. But this is not necessarily coupled to this rebellious way of thinking, the movement and the pictures, this is the religious or spiritual approach.
Satanism is a winged word in todays linguistic usage, often used for things which have nothing to do with satanism or satanistic thoughts like some conspiracy theories about satanistic-judo NWO stuff or robbing graves which is also considered a "satanistic act" by some people who bringt this in connection with some devilish act or something like that. I would consider it in most cases an act of smattering but that is just my personal thought.
Well, I finally should add that this is the way I mostly experienced satanism (and actually practiced it myself for a while) and the impression I got from the people I spoke with and the literature I read about it. The part with the flashy pictures is the biggest and most present one as far as I know, the theistic satanism and devil worshipping is actually pretty small and often fuses with chaosmagick approaches or other things. But of course this is also the most mysterious and interesting part for many outsiders which associate satanism in general with this small part (and the most "evil" part [twisted] )
I hope this helped you a little bit to get your own picture about this topic.
As literature I would recommend everything written by
Oliver Fehn as well as
Michael W. Ford - Scales of the Black Serpent.
I would also have some literature tips about "satanic-black" practice which might also be interesting but I guess for now this should be sufficiant.
Ramscha