A credential-on-file transaction is another name for a stored credential transaction: a card payment in which the merchant or its payment provider uses card details saved earlier with the cardholder's agreement, rather than asking the cardholder to enter them again. The main entry explains the scheme rules in detail.
"Credential on file" (often shortened to COF) is wording widely used in the card industry and in merchant contracts, while Visa's framework is usually described in terms of stored credentials. Both describe the same framework. The first payment, in which the details are saved, is the initial stored credential transaction; later payments are either started by the cardholder, such as a one-click checkout, or by the merchant, such as a subscription charge, known as a merchant-initiated transaction.
Flagging these payments correctly in the authorisation message helps issuers recognise them, improves approval rates and affects how strong customer authentication rules apply. The practice of storing the details themselves is described under card-on-file.