Like others are saying, it is a new york thing. But in general, upstate means further from the city than where the speaker lives. Until you crouse some imaginary line, then downstate means closer to the city. Comonly, but not always, it is used in a derogatory sense. They city people think the upstaters are rural hicks. And the upstaters think the city people couldn't survive outside a city.
Source, I grew up in an area that didn't consider itself upstate, but all the city people sure did.
Yes but also when people are telling someone they're from New York they tend to assume the city, so the follow-up answer is for clarification. The state is big and wildly different from NYC