I always handled it as:
Mountain Dwarves = Tolkien Stereotype. Living in the great halls of mountains, culture of experienced miners, often gruff and somewhat xenophobic, possibly a bit greedy. Thorin is the archetypal Mountain Dwarf.
Hill Dwarves = The dwarves that got used to living with other people. They are hanging out in your cities with many other races, possibly as merchants or blacksmiths, but ultimately cosmopolitan compared to their isolationist mountain cousins.
So basically "This one culture group stereotype" and then "All the other guys in general."