Greater New York vs New York State

Greater New York and New York State both are nouns.

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

Greater New York (noun)	New York State (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	a Mid-Atlantic state; one of the original 13 colonies, with capital Albany