Under a four-party card model, responsibility is divided between the institution that issues the card or payment account and the institution that equips merchants to accept card payments. The other participants are the cardholder and the merchant or other party accepting the card. Cash withdrawals are commonly handled through an automated teller machine made available by the acquiring institution. In a three-party model, issuing and acquiring are undertaken by a single organisation.
Source: European Central Bank (ECB) (source). This glossary entry is an independently worded adaptation of the cited information.