Mexican vs greaser

Mexican and greaser both are nouns.

Word	Noun	Adjective	Verb	Adverb
Mexican	Yes	Yes	No	No
greaser	Yes	No	No	No

As nouns, greaser is a hyponym of Mexican; that is, greaser is a word with a more specific, narrower meaning than Mexican:

Other hyponyms of Mexican include Taracahitian, Chicano, taco, wetback, Mexican-American, Mexicano.

Mexican (noun)	greaser (noun)
a native or inhabitant of Mexico	(ethnic slur) offensive term for a person of Mexican descent

Mexican (adjective)	greaser (adjective)
of or relating to Mexico or its inhabitants