Yeah, I thought they were the same, guess not?
They are the same. satan is more of a title meaning "The Adversary". it's apparently a really common misconception but i was always taught that satan and lucifer were the same.
Edit: I've looked into it and more convinced lucifer is descriptor, of course meaning morning star, than an actual name or demon. it was used in Isaiah to describe the drastic fall of a king and in 2 Peter, it was a descriptor for Jesus.