Nope. The grizzly is actually a type of brown bear; they're not synonyms.
Kodiak is another subspecies of brown bear.
From the link below:
While there has been much confusion about the taxonomy of brown bears (Ursus arctos), taxonomists agree there are at least two subspecies in North America -- the grizzly bear (U. a. horribilis) and the Kodiak bear (U. a. middendorffi).