The customer is the one who receives the card from the issuer. They initiate the transactions by purchasing goods or services from the merchants.
The merchant is the one providing the customer with services or goods in exchange for money.
The acquirer is the financial institution processing transactions on behalf of the merchants. They are enabling the merchants to accept card transactions. The acquirer is responsible for exchanging the funds with the issuer, on behalf of the merchant.
The issuer is the financial institution providing the cards to the customers. In order to do so, they collaborate with card schemes, such as Visa or MasterCard