I think you are misleaded by the branding on your debit card. Most transactions are not going through Visa, but a third-party solution that the banks them selves run. I might be wrong, but I think Nets delivers the solution in most of northern Europe. They call it NetAxept.

This is a direct pay solution used with online terminals, the Visa/MasterCard-part of your debit card is just for offline transactions or credit.

There are quite a few different payment processors here (Nets, PayEx, BABS, Dibs...), not really sure about how the backend works between banks. My card works in anything with a Visa logo, but there's no credit connected to it.

I don't get it. NetAxept appears to be some kind of payment processor for web shops; certainly not something a bank would use for its internal processing.

It would be the height of stupidity for Mastercard and Visa to allow banks to issue cards with their labels and then have these cards be part of some secret "strictly Northern Europe" Mastercard/Visa network. Talk about confusing the customers.

But this is all moot: I have both Mastercard and Visa debit cards issued in Sweden. They work perfectly well outside of Europe...

In Finland the banks recently dismantled the old debit card system and forced everyone onto the insecure (EMV based) and expensive Visa/MasterCard branded debit cards. You still sometimes see the old cards but banks have stopped issuing new ones.