From what I read on Wikipedia, grizzlys are a subspecies of the brown bear:

The grizzly bear (Ursus arctos horribilis), also known as the North American brown bear or simply grizzly, is a population or subspecies of the brown bear inhabiting North America.

Family: Ursidae
Genus: Ursus
Species: U. arctos
Subspecies: U. a. horribilis