>>There's a city of New York and a New York City, but I've never heard of a city of New York City.
>
>Never mind the third, just be kind and explain the difference between the first two, and between New York and New York City. Separately, if possible. TIA.

Like all things New York, it's complicated.

New York - to a New Yorker - means New York state, including cities such as Albany, Syracuse, Buffalo, etc.. To most of the people I know who are not New Yorkers, New York means New York City.

New York City - to a New Yorker- means the five boroughs, or counties - Manhattan, Queens, Bronx, Brooklyn and Staten Island (to confuse things more they are sometimes called New York, Queens, Bronx, Kings and Richmond.) I grew up in Queens. That made me a resident of New York City and subject to New York City taxes.
A police officer in any of the boroughs is member of the NYPD (New York City Police Department), likewise for a firefighter and the NYFD.

To most of the people I know who are not New Yorkers, New York City means Manhattan.


The City of New York is a term that is used on legal documents instead of New York City e.g. The people of the City of New York vs x.