They’re not different masks at all. They’re completely different beings.
Now, Satan is a being made of parts of other spirits (like Lucifer), but he has his own parts too. This has also been said by Lucifer and Satan themselves (you can find more info on that in the forum, we have lots of threads for this matter).
I mean, it’s a way to see it. Lucifer is known as the emperor and Satan as a great godlike being, so, it’s not wrong to assume that.