Greater New York vs city

Greater New York and city both are nouns.

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

Greater New York (noun)	city (noun)
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	people living in a large densely populated municipality
	a large and densely populated urban area; may include several independent administrative districts
	an incorporated administrative district established by state charter