You can choose at the register how you want to use the card, there are buttons on the machine or on-screen choices for 'Debit' and 'Credit' . There can be a limit imposed by the bank on how much you can process in a single transaction as a debit (I suppose to limit losses if it's stolen).
Edited for clarity.
Yes, I understand that - but how can one card operate presumably two accounts? Are both account details loaded onto the card somehow? How do the mechanics work?
A debit card here debits money from your current account.
A credit card adds the cost of the item onto a running balance which you then pay off at the end of the month (or whenever).
They're totally separate things.
Are they not, over there? Are they something different?
I have a "check card" from my bank that can be used as either a debit or credit (Visa) transaction.
When I choose to have it run as a debit card, I have to enter my PIN, and I'm usually given the option of requesting cash back. The transaction shows up in my account statement and is labeled as a debit transaction.
When I choose to have it run as a Credit transaction, then from the store's perspective, it's as if I was using a Visa credit card. If the amount of the transaction is above whatever threshhold is set by the store (and possibly part of their merchant agreement with Visa) I have to sign a receipt. The transaction appears on my account statement and is labeled as a Visa transaction.
The advantage for me is that I can use the same card at any place that accepts Visa, and at any place that accepts debit cards (even if it doesn't accept Visa).