Magical Beast

In the world of Fate/stay night, a general term for beasts which do not correspond to normal ecosystems.
They are divided into three ranks: monstrous, mythical, and divine.
The vast majority of monstrous beasts are crossbreeds (chimera) living in still-uncivilized regions, but it seems that those of mythical rank and above have shifted to the far side of the world.
Though the Pegasus that appears in the story is a monstrous beast, its long life puts it at the level of a mythical beast. Ordinary magi are completely unable to compete with something of this rank.
Also, beings that take after dragons are considered to be superior, regardless of classification. Since dragons are endowed with the characteristics of several species, it appears that even consorting with humans was not uncommon.

Fate/side material: Fate Encyclopedia