twenty dollar bill vs greenback

twenty dollar bill and greenback both are nouns.

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

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

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

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