Could be considered different aspect of the same thing?
Different energies from the same Source?
What ties these entities together is the independence aspect. But, no, I wouldn’t say they’re multiple faces of the same force. Not necessarily, at least.
Satan represents the adversarial force - that which goes against the grain. It can also means the accuser. In the adversarial sense, Satan is rather vague.
Lucifer represents the emerging consciousness, the emerging light, the bringing of light, the moment of lucidity from the darkness, enlightenment, etc.
Belial means either without value, or he without a master. His gifts and specialty differ from Lucifer and Satan.
Leviathan is a large, and powerful sea creature. Among other interpretations, he’s the personification of sheer power that’s capable of unleashing Hell (no pun intended).
So while these entities have some similarities, they differ quite a bit from each other.