Mexican vs Chicano

Mexican and Chicano both are nouns.

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

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

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

Mexican (noun)	Chicano (noun)
a native or inhabitant of Mexico	a person of Mexican descent

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