[joopxiv]

Depending on the category of the merchant, the network charges an interchange fee, the cost of which is split between the issuing bank (which takes most of the cut), the card association, and the acquiring bank.

This isn't entirely correct. The interchange is the part of the transaction fee that goes to the issuer. The card network gets a scheme fee, and the acquirer/processor charge a fee on top of that. If a merchant pays the same rate, regardless of what type of card is used, (credit/debit, consumer/business) then the processor or acquiring is basically rounding up.