At some gas stations' pumps I get the cash price when using a debit card.
I think the government regulated those recently. That should have been left alone just like credit cards. Once the fees are high enough the market will create cheaper alternatives especially in the age of the internet.
I think debit cards ave smaller fees. “
If you are a merchant that accepts credit cards there are all kinds of fees that are charged, depending on the means you use to process the card. The new Square charges a flat fee regardless. On-line terminal input of recurring charges charges less for debit cards but way more if a card has a special program linked to it - like the airline mileage accumulator. Just depends and there is no way to tell what the percentage will be until you check your monthly statement.
Convenience matters more to customers than what the merchant is being charged - unless you happen to be one of those merchants.