Ursus arctos is a species properly known as the brown bear. It includes a bunch of subspecies: Himalayan Brown Bear, Atlas Bear (extinct), North American Brown Bear (aka “grizzly”), Kodiak Bear, Eurasian Brown Bear, and others.

“Grizzly” is a colloquial name for two subspecies (if you count the extinct California Grizzly). The species is brown bear. “Brown bears” definitely exist.