Originally referring merely to the registry of transactions (deposits, withdrawals) for a fund held by a bank, the sense came to encompass the fund being held.

bank account (plural bank accounts)

1. A fund, held by a bank in a contractual arrangement between the bank and the owner of the fund, a customer of the bank, into which they can deposit and from which they can withdraw money.

• Swiss bank account

• current account / checking account
• deposit account
• savings account
• bank statement

• “bank account”, in OneLook Dictionary Search.
• William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “bank account”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.