Good question, the easy answer is both. Both the large bears you will see in Alaska and the smaller bears you might have seen at Yellowstone are not only the same species, but the same subspecies, Ursus arctos horribilis. The brown bears found on Kodiak are considered a different subspecies, primarily because of some differences in the skull. In general, bear biologists and those interested in bears tend to call the bears in Alaska brown bears, and those found in the Northern Rockies of the United States and Canada Grizzlies. The term grizzly comes from the silver tipped hair of the bears in the Rockies.
However, based on sizes, diet, and home ranges some biologists have recommended designating 3 groups of brown bears whose ranges are mapped below. The 3 groups described from studies of 25 different populations were the Coastal, the inland, and the barren ground brown bears. In Alaska, both in Katmai and Silver Salmon Creek, you are seeing the Coastal Brown, the largest of any of the brown bears found in North America or the world. There are large coastal brown bears in the former Soviet Union in Kamchatka as well.
(From Effect of energy availability, seasonality, and geographic range on brown bear life history by Steven H. Ferguson and Philip D. McLoughlin; Ecography, Copenhagen, 2000.)