By that logic you would count Vail/Beaver Creek, Breck/Keystone/A-Basin, Squaw/Alpine, Alta/Snowbird or Brighton/Solitude as one.
Alta/Snowbird is a tough one, because you can ski from one to the other. Still, most people count them as 2 separate. I don't see the reason for that but nonetheless counted them as two, if only because of tradition.
Brighton and Solitude don't even share the same lift ticket. So can't be "one".
A-basin/Keystone/Breck are more like Brighton/Solitude.. Not linked by lift. And while you can get "combined" tickets. The single area ticket, especially with A-Basin, is cheaper than the combo ticket. That's really not the "same" mountain.
Basically, I used same criteria as Phil:
IMHO, If they are connected with a lift, they can be considered the same...Park City/Canyons or Sugarbush/Sugarbush North as examples or It they combine the skiable acres together as the default. If a seperate lift ticket can be purchased, they are different areas.
Squaw/Alpine and Park City/Canyons are borderline. They used to be definitely separate. But they got combined. In Park City's case, I tend to consider it "one" because I do ski from one to the other and back. You can't even buy Park City only tickets any more. With Squaw-alpine, it really qualify as "two" because they're not linked by lift. But since you can't buy ticket for just one without including the other, it's..."one"!
But yeah, there're exceptions. It gets complicated. .