My limited understanding-

Companies have to pay a fee when someone makes a purchase with a credit card, so gas is generally slightly more expensive with credit card transactions vs cash (and maybe debit?).

If you pay with a debit card, you're not borrowing money, so I guess it's closer to cash than it is to credit. In my area, they don't let you buy lottery tickets with credit cards but you can buy them with debit cards, which I suppose is a good thing. Not sure how gas prices are affected when you pay with debit.