New York vs city

New York and city both are nouns.

Word	Noun	Adjective	Verb	Adverb
New York	Yes	No	No	No
city	Yes	No	No	No

New York (noun)	city (noun)
a Mid-Atlantic state; one of the original 13 colonies, with capital Albany	people living in a large densely populated municipality
the largest city in New York State and in the United States; located in southeastern New York at the mouth of the Hudson river; a major financial and cultural center	a large and densely populated urban area; may include several independent administrative districts
one of the British colonies that formed the United States, with capital New York City	an incorporated administrative district established by state charter