A card issuer processor is the full descriptive name for an issuer processor, the firm that provides the technology behind card issuing on behalf of a card issuer, and that entry covers it in detail.
The processor approves or declines transactions in real time against the cardholder's balance or credit limit, applies spending controls and fraud rules, manages card records and PINs, handles clearing files from the networks, and supports disputes, statements and reporting. Banks may run these systems themselves, but many outsource to processors, and most fintech card programmes rely on modern API-based processors working with a program manager and a sponsor bank. Some providers bundle processing with other services in a card-as-a-service offering.
"Card issuer processor" and "issuer processor" mean the same thing; the longer form is used where it is not clear from context that cards are meant. The opposite side of the card transaction is served by the acquiring processor, which works for acquirers and merchants.