Payment processor
The company running the technical machinery behind a card payment on behalf of an acquirer or issuer, without owning the relationship with the merchant or cardholder.
In the four-party model it looks as if acquirer and issuer talk to the card network directly. In practice many banks outsource the job to a processor, which accepts authorisations in ISO 8583, routes them onward, assembles clearing files and works out the fees. The industry distinguishes acquiring-side processors, such as First Data and Worldpay, from issuer processors, which run card accounts, PINs and fraud checks for banks that would rather not build it themselves.
The boundaries are blurry. In the US, "processor" often means anyone who takes card payments for a merchant, and a PSP like Stripe is processor, gateway and sometimes acquirer at once. Consolidation has been brutal: Fiserv bought First Data and FIS bought Worldpay, both in 2019.