Appalachia has been inhabited by European- and African-Americans since the 1700s. It has a very, very distinct culture, rooted in the Scots-Irish Protestant identify of the first white settlers, with contributions from various Native American nations (foodways, folk medicine, local toponyms, etc), free blacks who fled the Lowland South to scratch out a living of their own, and later waves of people who trickled in. It's adjacent to Southern culture but very much its own thing. Often characterised from without and within by stubborn pride, distrust of outsiders, self-reliance, familial loyalty, fierce independence, and capable of both nihilistic debauchery and ardent piety.

The Rockies were settled by whites much later, and really didn't coalesce into a distinct region of the US until around the turn of the 20th Century. Telegraph, radio, and railways were always there to connect inhabitants to the civilised world back east, so there was no period of isolation for a truly distinct local identity to really form. Whereas someone from West Virginia or Kentucky will tell you with pride about how many generations their family has lived in those same hills and hollers (hollows), most people in Colorado are relatively recent arrivals from elsewhere, with the exception of Mormons who settled the region before the civil war, but that's another matter entirely. So someone from elsewhere in the US or Canada can settle in the Rockies and probably feel quite at home, as the culture there is much less distinct from the mainstream Anglo-American culture. Whereas Appalachia is more likely to feel like another world of you weren't born there.