Sans, Gaster, and Papyrus are skeletons and all are brothers
Papyrus is the king of monsters
Sans is technically the Prince and I guess that's the same for Gaster
Toriel and Asgore are humanoid goats and their Dad, Asriel, was shattered across time and space being lost forever... and everyone frogot him except for Toriel, for some reason she can have very faint visions of him
Asgore is a royal guard in training but he has considered to be in the guard