I've had both VISA and MasterCard debit cards, delivered from my Swedish bank. Both had 16-digit card numbers, not my bank account number.
The only hick-up is that they default to 2FA: using a smartphone (domestic bank system) or card-reader (chip-and-pin). My bank has supplied me with a small card-reader for home use, which I also use for on-line banking.
To order from an on-line vendor that does not support chip-and-pin, I'd have to also log into my bank and temporarily enable "Internet payments".
This has worked for me every time I've ordered from US, Australia or Japan.
The only hick-up is that they default to 2FA: using a smartphone (domestic bank system) or card-reader (chip-and-pin). My bank has supplied me with a small card-reader for home use, which I also use for on-line banking. To order from an on-line vendor that does not support chip-and-pin, I'd have to also log into my bank and temporarily enable "Internet payments". This has worked for me every time I've ordered from US, Australia or Japan.