twenty dollar bill vs bank bill

twenty dollar bill and bank bill both are nouns.

Word	Noun	Adjective	Verb	Adverb
twenty dollar bill	Yes	No	No	No
bank bill	Yes	No	No	No

As nouns, bank bill is a hypernym of twenty dollar bill; that is, bank bill is a word with a broader meaning than twenty dollar bill:

Other hypernyms of twenty dollar bill include bank note, banker's bill, banknote, bill, Federal Reserve note, government note, greenback, note.

twenty dollar bill (noun)	bank bill (noun)
a United States bill worth 20 dollars	a piece of paper money (especially one issued by a central bank)