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This is known as 'Framing' in psychology and behavioural economics.
Credit Card Fees were once all told to the customer and seen as a tax on using credit card which nobody feels good about, the way it was resolved was by instead referring to that tax as a discount to those people using debit cards. In modern times there normally isn't any difference like you say, but this is the way it was combatted originally. This way, people don't feel hard done by using their credit card at all and continue to use it over the debit card.
Also, for the love of God don't make your credit card fee transparent - I've used a bunch of places recently and all it does is make me feel annoyed. I paid something like £70 extra recently to pay with a credit card (work on the car) than it would have cost with a debit card.
I'd far rather the garage had set it's pricing so they made a little extra if I'd paid with a debit card, rather than giving me a very irritating additional charge, on top of a large primary charge - which was the very fucking reason I decided to put it on a credit card.
i.e. quote a single, fixed price - don't fuck around with additional charges, add VAT afterward, or any other douche bag behaviour.