[thekevan]

Plenty of times I have mentioned being from Rochester, NY when in Florida or California. People there often assume it is a part of or suburb of NYC. Even after I have told them I am a 7 hour drive from the city and never even visited it until after I moved to Washington DC at 26.

Wikipedia even notes the differentiation is important.

"The city is referred to as New York City or the City of New York to distinguish it from the State of New York, of which it is a part"