Eh, it's a pretty big distinction weather-wise. Extreme Western New York and the Tug Hill plateau are all susceptible to somewhat frequent lake effect snow. Given the right time of year and wind fetch, you can see narrow convective / lake-effect snow bands from the Finger Lakes. But broadly speaking the actual annual expected snow and the phenomenology of the storm systems that produce that snow are very different over the rest of the state.
When I lived in NYC I used "upstate" to mean anything not in the five boroughs, Long Island or Westchester, and I don't think this usage is uncommon.