billfold vs. wallet

a thin, flat, folding fold case, often of leather, for carrying paper money in the pocket and with fewer compartments than a wallet.

wallet ( def 1 ).

a flat, folding pocketbook, especially one large enough to hold paper money, credit cards, driver's license, etc., and sometimes having a compartment for coins.

Chiefly British. a bag for carrying food, clothing, toilet articles, etc., during a journey; knapsack or rucksack.