Ursus arctos is the name of common brown bear, which has population all over the northern hemisphere. Then there are all kinds of third parts to the name, defining sub-species.
Ursus arctos horribilis is actually grizzly bear, it's bigger than normal brown bear. Kodiak bear is
Ursus arctos middendorffi [sic].
American black bear is
Ursus americanus, and polar bear is
Ursus maritimus, etc. etc. In general, bears belong into family Ursidae, and what is usually conceived as "bear" would be members of subfamily Ursinae...
What is disturbing is that I didn't need to use wiki to remember these ones. Nevertheless,
here's the wiki link...

Damn, aldo was faster.