billfold vs wallet

billfold and wallet both are nouns.

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

As nouns, billfold and wallet are synonyms defined as:

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

Other synonyms of billfold include notecase, pocketbook.

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