Is there a difference between Lucifer and Satan?

I've always thought of it as, Lucifer is the name for the devil while he was God's angel. However when he turned evil, his name became Satan.

Satan comes from the Hebrew "HaSatan" which means the "Opposer". His job, as an angel, was to oppose the Will of God and call it into question, but HaSatan is not his name, just his function. (This is similar to the term "President" which is not a name, but a function.) Christians gave the Opposer the name Lucifer.