Croton bug vs cockroach

Croton bug and cockroach both are nouns.

Word	Noun	Adjective	Verb	Adverb
Croton bug	Yes	No	No	No
cockroach	Yes	No	No	No

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

Croton bug: small light-brown cockroach brought to United States from Europe; a common household pest
cockroach: any of numerous chiefly nocturnal insects; some are domestic pests

Other hypernyms of Croton bug include roach.

Croton bug (noun)	cockroach (noun)
small light-brown cockroach brought to United States from Europe; a common household pest	any of numerous chiefly nocturnal insects; some are domestic pests