Puerto Rican vs American

Puerto Rican and American both are nouns.

Word	Noun	Adjective	Verb	Adverb
Puerto Rican	Yes	No	No	No
American	Yes	Yes	No	No

As nouns, American is a hypernym of Puerto Rican; that is, American is a word with a broader meaning than Puerto Rican:

Puerto Rican (noun)	American (noun)
a native or resident of Puerto Rico	the English language as used in the United States
	a native or inhabitant of the United States
	a native or inhabitant of a North American or Central American or South American country

Puerto Rican (adjective)	American (adjective)
	of or relating to or characteristic of the continents and islands of the Americas
	of or relating to the United States of America or its people or language or culture