It helps to recall that the term account refers to a record of transactions, whether current, past or future, and whether in money, or shares, or other countable commodities. Originally a bank account just meant the record kept by a banker of the money they were holding on behalf of a customer, and how that changed as the customer made deposits and withdrawals (the money itself probably being in the form of specie, such as gold and silver coin).
Some customers will keep their own records of their transactions, for instance, so they can check for errors by the bank. That record kept by the customer is also an account, of the money the bank is holding for them. When that customer is another bank, since they also keep other accounts (of the money they are holding for their customers) there is a need to clearly differentiate between these two types of accounts.
The terms nostro and vostro remove the potential ambiguity when referring to these two separate accounts of the same balance and set of transactions. Speaking from the bank’s point-of-view:
- A nostro is our account of our money, held by you
- A vostro is our account of your money, held by us