Bank fees are account charges. Merchant fees are what a card processor keeps from each payment, usually a percentage plus a fixed amount per transaction.
Why they are worth examining
A few percent of every card payment is a few percent of revenue, and revenue is a much larger number than anything else these get compared against.
Owners routinely spend an afternoon on a supplier price and never look at processing, because it arrives netted off rather than as a bill.
What drives the rate
Card type. Commercial and rewards cards cost more than standard debit.
How the card is taken. Keyed-in and online rates are higher than tapped-in-person, because the fraud risk differs.
Volume and average ticket. The fixed per-transaction component matters enormously on small payments and barely at all on large ones.
The trade worth making anyway
The fee is smaller than the cost of the delay it removes. An invoice paid in three days at a small percentage beats one paid in forty at no cost — see collections, where payment speed is usually the largest recoverable number in the business.
Surcharging is legal in some places and not others, and tends to cost more in goodwill than it recovers.
Where it sits
Under professional and banking in your accounts, as overhead. Some businesses treat merchant fees as a reduction of revenue instead — either is defensible, and doing it the same way every month is what matters for a comparable gross margin.