Satanism is not part of Paganism anymore than jelly is part of peanut butter. Yeah, They both go on bread and have similar aspects but in no way represent each other.
Satanism is also not a belief system born out of the Bible. It has nothing to do with Christianity, Nor is it adversarial to Christianity, But instead it defies and denies all religions who spook people with eternities in hell, And eternal bliss's in a heaven.
Satanism is really about freedom. Satanism is about complete individuality. It believes that people should do whatever they want to do as long as they do not hurt others. It also believes that some people are better than others and that they shouldn't be punished if they rise to the top, While those who are untalented stay at the bottom.
There is a fake Satanic movement that is laughed at by Satanists. This fake movement is usually followed by young people who sacrifice animals, Wear black clothes, Distance themselves from others, And in some cases kill people.
Satanism has roots in Sethianism and other night time magical movements. Most of the magical movements of the past communed with deities of the daylight, While Satanists, At least the roots of Satanism, Communed with the spirits of the night. And yes, There is usually more sex, More partying, And more freedom when dealing with night-time culture than day time culture.
I don't know what Satanism you are referring to but the one depicted in the photograph is LaVeyan Satanism which was founded by Anton Szandor LaVey back in the 60's. LaVey Satanism is more of a philosophy and does not associate with Paganism or religion at all. If you read the satanic bible or know anything about this satanism you would know that they do not worship the devil and heavy metal, Cutting, And dressing in all black is just a way of life. LaVey Satanism is just a spiritual religion that rejects some of modern life's ideals. If you are referring to devil worshippers, They probably do refer to themselves as pagan, Or not. Who knows.
In the bible the people of Israel had to do war with the real pagans because they were wicked and sacrificed their children. There was also strange diseases at the time so they had to destroy certain houses and in some cases wipe out the livestock to prevent contamination.
The pagans worship the stars earth creatures and entities like Gaia and the holy mother. Blah blah.
Today's pagan are nothing like the evil original pagans of the past. They are just a pale copy.
Actual Satanist are people who worship the devil directly. Those people exist and they behave like normal people and are respectable people in society. Not every Mayor or high ranking official is a satanist, But they are out there. They cover their tracks well and leave no evidence. They are the most dangerous people of all.
The most common satanist though are just young weirdos who want to be rebels and look cool. They do not believe in an actual Satan and just like heavy metal and wearing all black. Those are the most harmless people who cause no trouble to anyone except for themselves.
So one hugs trees and maybe cuts themselves worshiping rocks and the other wears all black and listens to heavy metal. They have no power at all.
Modern Satanists don't agree that they are a part of Paganism. They don't think that they are a part of Satanism. They also are involved with Satan which is a christian ideology so that makes them a branch of Christianity even tho they are anti christian. These all contribute to they're belief that they aren't Christian.