In a lot of cases the processor is not the bank (SmartPay, Square, etc), so usually, yes, they'll want a cut. And then you'll also get charged for the paper rolls (for receipts), and renting of the EFTPOS equipment if you rent it.

I ripped this off some marketing material that I found for a popular EFTPOS terminal in Australia:

A merchant service fee is a fee you pay to your EFTPOS provider to process your transaction payments. This fee is calculated as a percentage (or fixed fee) of every transaction where a customer swipes, inserts, or taps their card at your terminal.

For every transaction, your bank pays fees which include: a fee to the issuing bank (e.g. the bank that issued the card), the scheme fee (e.g. Visa, Mastercard, EFTPOS), and the switch fee (who processes the transaction).