'Lucifer' is a latin translation of the Hebrew word for "morning star", used to mock a king of Babylon in the Old Testament. 'Satan' is a Hebrew word used to describe an angel or some type of 'accuser' sent by god to screw with various people. In Christian fanfic this turned into Lucifer/Satan being some sort of fallen angel that tries to make people be evil. There's not really much biblical evidence for this interpretation.