I used to have an online maestro card (was solo and now known as debit mastercard) and an offline card (was switch, now also known as debit mastercard) from a UK bank, due to having two current accounts there.
The offline card was from a current account with an overdraft and also worked as a cheque guarantee card, for cheques up to £250 under the (discontinued ~2011) cheque guarantee scheme[0] and had a special hologram on the back. The retailer would watch you sign the cheque and write details about you, the card and any CCTV etc. on the back of the cheque. I imagine the offline behavior of the card was similar, and was a carry over from that.
The online card was from a basic account with no overdraft facility and acted a bit like a prepaid debit card.
The offline card was from a current account with an overdraft and also worked as a cheque guarantee card, for cheques up to £250 under the (discontinued ~2011) cheque guarantee scheme[0] and had a special hologram on the back. The retailer would watch you sign the cheque and write details about you, the card and any CCTV etc. on the back of the cheque. I imagine the offline behavior of the card was similar, and was a carry over from that.
The online card was from a basic account with no overdraft facility and acted a bit like a prepaid debit card.
[0] https://en.wikipedia.org/wiki/Cheque_guarantee_card