Satan was the serpent in the Garden Of Eden, the Devil, the First of the Fallen.
When Lucifer lost the war in Heaven and was cast down, he found Satan was already there, waiting for him. Satan gets to walk the Earth and even pops up in the Book of Job, visits the Lord with the angels.
Lucifer, Beelzebub and Mephistopheles form the Truimvirate of Hell.
Lucy is a Fallen Angel, the Morningstar. Satan is The Devil. Most people confuse the two.