Satan, Lucifer, Beelzebub... All the same person. Angel cast out of heaven. He wasn't the only one. There were also the Irin "watchers", which if I am correct totalled 200, which came to earth and married/mated/bred with human females which created the Nephilim. It's all Old Testament stuff. Book of Enoch shit. It really depends on which version of the bible you read as well, as even though they all teach the same sorta thing some teach more than others. You also have the story of Lilith who was the first female who was made as Adam's equal who left the garden to walk amongst angels and demons. She also took Cain under her wing after he was cursed by god after killing his brother. I am a baptised Roman Catholic but we do not learn this shit, not is it in the catholic bible. I had a high school teacher who was doing a doctorate in that sorta shit who brought up all the different stories from the same book as well as stuff which never made the current bible, remembering that back in the day (before and or around the time of the Roman Empire)a big ass group of people came together and decided what will be in the bible in attempts to "unify" the many variations of the book.

I'm fairly sure Lucifer was Satan's old name. Or an alternative name, like Yahweh.

Lucifer is the Angel who fell out of God's favor and was cast out of Heaven. Satan is the ruler of hell and evil incarnate. They're essentially the same person, as far as I can tell.