American cockroach vs cockroach

American cockroach and cockroach both are nouns.

Word	Noun	Adjective	Verb	Adverb
American cockroach	Yes	No	No	No
cockroach	Yes	No	No	No

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

American cockroach: large reddish brown free-flying cockroach originally from southern United States but now widely distributed
cockroach: any of numerous chiefly nocturnal insects; some are domestic pests

Other hypernyms of American cockroach include roach.

American cockroach (noun)	cockroach (noun)
large reddish brown free-flying cockroach originally from southern United States but now widely distributed	any of numerous chiefly nocturnal insects; some are domestic pests