I think it's best to agree to disagree. In Australia you usually have a basic ATM card linked to your savings account, and/or a credit card which may also have your savings account linked to the card
for ATM access only. If you press 'savings' at a merchant terminal you're required to enter a PIN, and the funds come directly from your account; if you press 'credit' then you sign the transaction slip and pay your credit bill when it arrives.
A Visa-style debit card which draws Visa transactions directly from the funds in your savings account is fairly rare, in fact it's only recently that it has been promoted on TV here. I've never seen or heard of a Mastercard debit card here.
Obviously, different parts of the world have different products and use different terminology.
