Gulf of Mexico vs Gulf Coast

Gulf of Mexico and Gulf Coast both are nouns.

Word	Noun	Adjective	Verb	Adverb
Gulf of Mexico	Yes	No	No	No
Gulf Coast	Yes	No	No	No

Gulf of Mexico (noun)	Gulf Coast (noun)
an arm of the Atlantic to the south of the United States and to the east of Mexico	a seashore of the Gulf of Mexico