In your wallet you probably have two types of payment cards; credit cards with either the Visa or MasterCard logo and the bank card which goes with your current account. Usually the bank card performs multiple functions; it is a cheque guarantee card, it is an ATM card drawing directly on your current account and it is a debit card doing the same in retail transactions.
In its role as a debit card it works through the same mechanism as the credit card using the same organisations, Visa and MasterCard, and will display one of their logos on the front. However, unlike a credit card, it doesn’t attract the same transaction fee (I am not sure of the exact details). You wouldn’t normally notice because in most shops and online transactions the fee is absorbed by the retailer. The major exceptions are the travel industry and booking agencies who insist on adding it to the bill afterwards. It is their right and I suppose it means that if you do want to pay by some other method then the price is not loaded up front.
Now the catch. Many retailers don’t understand the difference between debit and credit and in travel agents you may find that they charge you the fee anyway (I have tried arguing and they still don’t understand and, at this level, don’t have the authority to change it). Similarly the online transaction pages don’t understand either, at least they appear not to.
Some years ago, debit cards had different logos on them, either Visa Delta or Mastercard Maestro. Web sites used to have a separate button for them which bypassed (or reduced) the fee. Some still do and it still works even though the logo no longer appears on the cards. So, if you have a Visa Debit card think Delta and if you have a MasterCard one, think Maestro and save money.
p.s. Visa Electron cards, which can be either Credit or Debit, don’t attract the fees and normally have their own button on web sites so are not affected.