I've noticed this before, but even NYS itself cannot decide on what regions are what:
All broken up by county, all different. So depending on who you ask, Cortland and Tompkins county could be CNY,Finger Lakes or Southern Tier.
The way I think of the regions of NY has more to do with the physical characteristics rather than random county groupings. For instance, Ithaca area is Finger Lakes to me, and Cortland is CNY. They are close, but vastly different in topology and feel.
Rochester and along the lake is classified and Finger Lakes or western NY, but bears little resemblance. It's flat, the land is more developed either agriculturally or industrially. The whole band from Buffalo to Syracuse from Lake Ontario to the thruway feels the same. Once you head down south, it's different, and Finger Lakes are definitely different than the areas to the east and west of them (the lakes have a big effect IMO). Then down south below them and close to PA it gets different again... similar, but drier, more like CNY.