city vs New York City

city and New York City both are nouns.

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

city (noun)	New York City (noun)
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
an incorporated administrative district established by state charter