Fees on the back end, what company transports the charge, and what authorization is used to authenticate it are all different.
With Credit, the money is not debited immediately. It is authorized immediately and held in pending until it is batched. It is only then that it is taken from the account.
When you use your PIN, it comes out immediately. The processing fees are lower on the back end, but the cost of entry is higher for the merchant and the level of risk to a consumer is greater (reference PIN sniffing routers that have been found).
It is only with the advent of cards that can be processed as both credit and debit (Visa's revenue is made up of mostly Debit processing fees from bank cards now, not credit) that this confusion has arisen.