water bug vs cockroach

water bug and cockroach both are nouns.

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

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

water 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 water bug include roach.

water bug (noun)	cockroach (noun)
a true bug: large aquatic bug adapted to living in or on the surface of water	any of numerous chiefly nocturnal insects; some are domestic pests
small light-brown cockroach brought to United States from Europe; a common household pest