Both words Satan and Lucifer have been horribly mistranslated from Hebrew. The deity of Satan who christians believe exists is someone they invented along the course of history.. The original hebrew phrase only appears twice in the original hebrew bible as 'the satan', and it means 'the adversary'. Both of the uses were not referring to a deity, but individual adversaries. In the book of job the word is used to refer to an angel God himself dispatched. I forgot where the other place the term was used was, but it was actually referring to a man then... it isn't important where it was, google it if you want to know.
From the two uses of the word, over time, Satan grew as a superstitious deity of opposition and fear in the minds of theists. As bibles were retranslated from one generation to the next scribes began substituting 'satan' in place of other conflicted oppositional words or phrases. Now what you have is a bible filled with the term 'Satan' apparently in reference to some diety which never infact existed.
The word 'Lucifer' comes from latin 'the luxfer' which in turn was a mistranslation / transliteration from the original hebrew phrase 'the light bearer' - a phrase which refers to the planet venus. Venus was referred to as the lightbearer as it often pops up over the horizon preceding the rising sun. Venus as a planet has always been associated with sensual indulgence. It is for this reason the mistranslation of venus into 'lucifer', a deity, stuck and embedded itself into the minds of theists - their superstitions regarding anything sensual in nature make them a very neutoric brand of people.
Satanism is really a naturalistic philosophy. It's all about appreciating ones animal nature. The name Satanism is really not relevant to the philosophy; this name was chosen to sardonically mock the biblical anxiety toward natural animal behavior. A real Satanist is not going to indebt himself to another diety, because that's contrary to his entire philosophy. Some people may actually pray or do rituals to Satan, but they are poseurs who have no clue what they are really thinking.
God/"Satan" (the dark side) have always been the same force, they have always ruled the world together.
