As I understand it.

Credit cards globally are dominated by a handful of networks, mostly Visa and Mastercard (and to a lesser extent AMEX and Diners). Debit card networks on the other hand tend to be more localised to a specific country or a handful of closely linked countries.

To give their cards broader reach debit card issuers often work with with credit card networks allowing their cards to be treated as a credit card. So when you take your US debit card abroad the terminals have no clue about the US debit card system, their "debit card" options will be for whatever debit card system they use locally, but they can process the card as a credit card.

As I understand it.

Credit cards globally are dominated by a handful of networks, mostly Visa and Mastercard (and to a lesser extent AMEX and Diners). Debit card networks on the other hand tend to be more localised to a specific country or a handful of closely linked countries. Some parts of Europe including the UK seem to be a bit unusual in that the Debit cards are actually primerally operated by the credit card networks.

To give their cards broader reach debit card issuers often work with with credit card networks allowing their cards to be treated as a credit card. Similarly in places where the credit cards and Debit cards are run by the same network the networks usually allow their debit cards to be treated as credit cards abroad. 

So when you take your UK debit card abroad the terminals have no clue about the UK debit card system, their "debit card" options will be for whatever debit card system they use locally, but they can process the card as a credit card.

As I understand it.

Credit cards globally are dominated by a handful of networks, mostly Visa and Mastercard (and to a lesser extent AMEX and Diners). Debit card networks on the other hand tend to be more localised to a specific country or a handful of closely linked countries.

To give their cards broader reach debit card issuers often work with with credit card networks allowing their cards to be treated as a credit card. So when you take your US debit card abroad the terminals have no clue about the US debit card system but they can process the card as a credit card.

As I understand it.

Credit cards globally are dominated by a handful of networks, mostly Visa and Mastercard (and to a lesser extent AMEX and Diners). Debit card networks on the other hand tend to be more localised to a specific country or a handful of closely linked countries.

To give their cards broader reach debit card issuers often work with with credit card networks allowing their cards to be treated as a credit card. So when you take your US debit card abroad the terminals have no clue about the US debit card system, their "debit card" options will be for whatever debit card system they use locally, but they can process the card as a credit card.