The word 'wallet' has been in use since
the late 14th century to refer to a bag or a knapsack for carrying
articles.
A billfold is a type of wallet carried by a man that folds over.
Billfold is one of those practical words that describe the function,
as folding bills. It is like the kitchen cupboard, which was
originally a wall attached board used to store cups and plates.
Americans call their paper money bills, even though they are really
Federal Reserve Notes. Other English speaking countries call them
notes.
Although billfold and wallet are used interchangeably, it is now
more common to use wallet. Technically, a wallet is the type women
usually carry in their purse. It has a long section where they can
put money without folding it
Wallets were developed after the introduction of paper currency to
the West in the 1600s. The first paper currency was introduced in
the New World by the Massachusetts Bay Colony in 1690. Prior to the
introduction of paper currency, coin purses, usually simple
drawstring leather pouches, were used for storing coins. Early
wallets were made primarily of cow or horse leather and included a
small pouch for printed calling cards.
During the 1800s, in addition to money or currency, a wallet would
also be used for carrying dried meat, victuals, treasures, and
"things not to be exposed". Wallets originally were used by early
industrial Americans. It was considered semi-civilized in 19th
century America to carry a wallet attached to the belt.
Incidentally, 'share of wallet' is a marketing measurement for the
proportion of money the customer spends on a product brand in
preference to the competing brands.
Bottom line, all billfolds are wallets, but not all wallets are
billfolds.