bad check vs bank check

bad check and bank check both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad check	Yes	No	No	No
bank check	Yes	No	No	No

As nouns, bank check is a hypernym of bad check; that is, bank check is a word with a broader meaning than bad check:

bad check: a check that is dishonored on presentation because of insufficient funds
bank check: a written order directing a bank to pay money

Other hypernyms of bad check include check, cheque.

bad check (noun)	bank check (noun)
a check that is dishonored on presentation because of insufficient funds	a written order directing a bank to pay money