Basically, there are three different groupings of 'discount rates' involved in credit card acceptance. The lowest rate is always charged whenever the customer's card is swiped with the magnetic stripe read on a machine.
A higher rate (often called mid-qualified) is charged if the cardholder's information is called in over the phone or key-entered.
The highest rates (often grouped into a category called non-qualified rates) are charged when the card is not present and information is key-entered. It is also charged when the deposits are not made on the same date as service was rendered. The card associations also charge a higher rate if the credit card that is used happens to be a business card or a corporate credit card.
These days, the actual credit card machines are smaller and less expensive than ever. Many of the machines are portable, allowing businesses in the service industry to take the machine with them on the job. This allows the smart business owner to get the "swiped" rate. Think about it: it pays to be able to get the lower swiped rate on the majority of your transactions.
There is no need to switch bank accounts to improve the way payments are accepted - it is the method or processor that is used that makes the biggest difference in what fees you will pay.