In Canada, debit cards are run by a not-for-profit venture founded by the major banks called Interac. Everybody's standard ATM bank card is usable as a debit card. This is the most common method of payment in the country.
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.
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...