Nostro account is the fuller name banks and treasury staff often use for what the Nostro entry calls simply a nostro: an account a bank holds with another bank, typically abroad and denominated in that other country's currency, so it can make and receive payments in that currency on behalf of itself and its customers. The two terms describe the exact same arrangement; "nostro account" is the plain-English version, while "nostro" alone is the shorthand bankers use in correspondent-banking and treasury conversations.
The full explanation of how a nostro account works, who opens one, how it pairs with a Vostro on the other bank's books, and how balances are reconciled is covered in the Nostro entry. This page exists because "nostro account" is the more common search phrase, and under Faisal's rule for synonyms, every distinct phrase a reader might type gets its own short pointer rather than being silently merged.
A Pakistani bank's US-dollar account at a correspondent bank in New York is a nostro account from the Pakistani bank's point of view: it is "our" money, held over there, used to settle dollar payments for the bank and its customers without the Pakistani bank needing a branch in the United States. The same account is a vostro account on the New York bank's books, since it belongs to someone else's customer.
For how nostro accounts fit into the Correspondent Banking Relationship (CBR), how banks track and match activity on them through nostro reconciliation, and how they relate to loro accounts, see the main Nostro entry.