In Christianity, Satan is a figure of evil, and the name Lucifer is often used interchangeably with Satan. This is not the view of self-described Satanists and Luciferians, however. These figures represent primal forces, freedom, and rebellion from dogma, among other things.
All three of these groups are considered left-hand paths, which is focused on self-determination and the power of the self, rather than submitting to a superior force. While Many Satanists and Luciferians do believe in a supernatural power, they see their relationship with them as more of a partnership than a mastery of a god over a subject.
While there are significant similarities between different types of Satanists and Luciferians, they are distinctly different groups.
The most well known branch of Satanism is the form created by Anton LaVey in the 1960s. He created the Satanic Bible, which remains the most available text on Satanic religion. He also formed the Church of Satan, which is by far the most well known and most public Satanic organization.
LaVeyan Satanism is atheistic. According to LaVey, neither God not Satan are actual beings. Instead, Satan is a symbol representing the qualities embraced by Satanists. Invoking the name of Satan and other infernal names is a practical tool in Satanic ritual, focusing one's focus and will upon certain concepts.
The only "god" in LaVeyan Satanism is the Satanist himself. Satanism is a celebration of the self. It encourages people to seek their own truths, indulge in desires without fear of societal taboos, and perfect the self.
Theistic Satanism, also known as Spiritual Satanism, recognizes the existence of supernatural beings. Oftentimes this being is called Satan, but sometimes other names are used. The Temple of Set is one of the most well known groups of theistic Satanists, although they no longer identify themselves as Satanic, seeing their movement as something new and distinct.
Regardless of the being or beings in charge, none of them resemble the Christian Satan. Instead, they are beings that represent the same general qualities as the atheistic Satanists associate with their symbolic Satan: sexuality, pleasure, strength, rebellion, etc.
Many see Luciferianism as another branch of Satanism (and generally a theistic branch, although there are some who see Lucifer as symbolic rather than an actual being). However, Luciferians see themselves as a separate religion.
Luciferians use the term "Lucifer" in its literal sense: "lightbringer" in Latin. Rather than being a figure of challenge, rebellion, and sensuality, Lucifer is a creature of enlightenment, the one who brings light out of the darkness.
He does not, however, present his gifts to everyone. Luciferians embrace the seeking of knowledge, delving into the darkness of mystery and coming out better for it.
Luciferians also stress the balance of light and dark and that each depends upon the other. Park of that light and dark pairing is spirituality and physicality. While Satanists revel in physical existence, and Christianity focuses more and spirituality, Luciferianism is a religion that seeks a balance of both, recognizing that human existence is an intersection of the two.