Yes, they are two completely different angels. However, in Catholic folklore, it is usually stated that Lucifer was the angel who led the rebellion in heaven against God, and that when he was cast down he was transformed into the dark angel Satan. Lucifer was beautiful to look upon, but Satan is said to be ugly to look upon. In modern Western occultism, Lucifer is considered to be the angel of light, and therefore the angel of truth and wisdom (enlightenment). He is the "light-bringer." Lucifer is more or less equated with the Greek titan Prometheus, who in myth is said to have brought fire to mankind, for which he was punished by being bound to a rock with eagles pecking at his liver. You can see the parallels between the folklore of Lucifer being cast down to earth as punishment for his disobedience, and Prometheus being cast down to earth as punishment for his disobedience. In Gnostic lore, the Serpent is the one who gave mankind the gift of knowledge. The serpent is usually identified with Satan, but in this context is more properly identified with Lucifer, the light-bringer. This is how Theosophy understands Lucifer. The Theosophists at one time even had a magazine titled Lucifer, which illustrates their understanding of this angel. How are we to sum all this up? Lucifer brings wisdom and thus freedom (free will) to mankind, and in doing so violates the will of the Demiurge, who is the god of this world (but not the Supreme God, the Source of Light). The Demiurge gets angry with Lucifer (the Serpent) for bringing wisdom to Adam and Eve and he throws them out of the Garden of Eden. He punishes Lucifer by casting him down (I know, I know, he's already been punished as leader of the rebellion, but couldn't the giving of mankind the gift of knowledge have been part of the rebellion, if we don't automatically assume that the revolt of the angels came earlier?) Having been cast out of heaven, Lucifer is regarded as having become ugly and is called Satan by some. But, Satan is actually the Adversary, and was always ugly. Satan is the one who tempted Job, and had a bet with the Demiurge that he could corrupt Job, which he lost. Lucifer never tempted Job. He would have helped Job understand that he shouldn't be loyal to a god who treats him like shit. Lucifer's whole deal is the Light-bringer -- he dispels ignorance by bringing the light of knowledge.