Two confusions dominate the public picture of Luciferianism, and they run in opposite directions.
The first is the collapse of Luciferianism into Satanism. There is real overlap: both are adversarial, both invert a Christian valuation, and individuals move between them. But the emphasis differs. Luciferianism foregrounds illumination, knowledge and refinement of the self, with Lucifer as teacher and liberator; Satanism in its dominant modern form foregrounds carnality, self-interest and the rejection of herd morality, with Satan as a symbol of the natural human animal. The Church of Satan rejects the distinction outright and treats Lucifer as simply one of Satan's names, which is itself evidence that the boundary is contested rather than agreed. A further difference is that Luciferianism contains a genuine theistic wing, while the largest Satanist organisations are formally atheistic.
The second confusion is far more consequential. Outside occultism, the word Luciferian is used mainly as a conspiracy term, denoting an alleged secret elite (variously Masonic, financial, political or entertainment-industry), said to worship Lucifer and to control world events. This usage descends directly from Leo Taxil, who invented a Luciferian Masonic order called Palladism in the 1880s and 1890s, complete with rituals and a fictitious high priestess, and who confessed the whole thing as a hoax in Paris in April 1897. The confession did not stop the material. It was recycled through twentieth-century anti-Masonic and antisemitic literature, through the Satanic Panic, and into contemporary online conspiracy movements.
The two senses of the word have almost nothing in common. Actual Luciferians are a small, decentralised, largely literary occult current with no political power and no institutional wealth. Being named in conspiracy literature is not evidence about the people so named, and the durability of that literature, more than a century after its author confessed to inventing it, is a fact about the audience rather than about Luciferianism.