If pay with debit card you are doing a bank transfer. Maybe in the US most people are using credit cards but in EU many are using debit cards.
The only difference is that one moves money from a credit account, the other moves it from a debit account.
The costs via Visa/MasterCard are broadly the same. The clearing and settlement process is also broadly the same. Neither are as quick or finite as a bank transfer. One big difference for a merchant is that debit/credit cards have a dispute process (called chargebacks), whereas bank transfers generally don’t.
They end up making an actual, real chip+pin authorized bank transfer.
Faster Payments (bank transfers in the UK) for example settle 3 times per day and are intended to be instant.
Debit cards usually settle daily and there can be a delay; which is why you will see an Auth on your account (card payments go; Auth to lock the money, Payment to set up the payment, and Settlement to move the actual cash). This is why the EU mandated banks start to show actual funds available (balance less all auths and other pending payments) as it can sometimes take days to settle debit card payments and people can be unsure of their balance.
In general, finance is an example of the "99 standards" error; in that every so often new standards come in to fix things but just add another approach to the mix (don't get me started on Direct Debits!)