dollar bill vs banker's bill

dollar bill and banker's bill both are nouns.

Word	Noun	Adjective	Verb	Adverb
dollar bill	Yes	No	No	No
banker's bill	Yes	No	No	No

As nouns, banker's bill is a hypernym of dollar bill; that is, banker's bill is a word with a broader meaning than dollar bill:

dollar bill: a piece of paper money worth one dollar
banker's bill: a piece of paper money (especially one issued by a central bank)

Other hypernyms of dollar bill include bank bill, bank note, banknote, bill, Federal Reserve note, government note, greenback, note.

dollar bill (noun)	banker's bill (noun)
a piece of paper money worth one dollar	a piece of paper money (especially one issued by a central bank)