I'm not sure what country the context is, but I remember using my mothers debit card in Sweden somewhere between 2000-2010 for online things without problems, as I only had a Maestro card at that point which didn't allow online purchases.
Are you sure you didn't use your mother's credit card instead? I also have one of these (embossed 16-digit card number, validity, CVC on the back) lying around, but those are the exception here rather than the rule. I literally only use it for things like online services in other countries. I believe with the country-wide switch from Maestro to V-Pay they should now also universally work for local in-store payments, but I don't think many people are actually using it like that - we're at 45 million yearly transactions for 18 million people.
No, 100% sure it was a debit card, as that's the only thing she ever used, and same for me, never owned a credit card in my life, still only have debit cards.
The debit cards my mom had and the ones I have now are identical to a credit card (including the 16 digit number, CVC and so on) except the fact that the money gets taken from the account directly instead of paying it at the end of the month (as I think credit cards do?).
Most big banks have their own TWINT apps, so that you don't even have to use it as a prepaid solution and it's instead directly linked to your bank account.
no idea if that's also how venmo/cashapp works.