As the website you referred me to indicates, the grizzley is a subspeceis of arctos, to wit, horribilis.
More importantly, horribilis is the only current member of Ursus arctos, much as man is the only member of homo sapien, and therefore the full designation "homo sapien sapien" is redundant, as is ursus arctos horibilis.
"Subspiecies" does not have a universally recognized taxonomic definition. As applied to ursus arctos, it merely is used to designate range.