Greater New York vs New York Bay

Greater New York and New York Bay both are nouns.

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

Greater New York (noun)	New York Bay (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 bay of the North Atlantic; fed by the Hudson River