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).
Now small cafes, tradies, etc getting on their feet can use the hardware they already have to start processing straight away.