wallet vs billfold

wallet and billfold both are nouns.

Word	Noun	Adjective	Verb	Adverb
wallet	Yes	No	No	No
billfold	Yes	No	No	No

As nouns, wallet and billfold are synonyms defined as:

wallet and billfold: a pocket-size case for holding papers and paper money

Other synonyms of wallet include notecase, pocketbook.

wallet (noun)	billfold (noun)
a pocket-size case for holding papers and paper money	a pocket-size case for holding papers and paper money