Yes, I am sure, at least in Italy.
Some Bancomat/Pagobancomat ones (but again not all of them) are connected to the IBAN (amd they sport both the IBAN and the name of the holder).
Many Bancomat/Pagobancomat are connected to Mastercard or Visa (or Maestro) debit cards and they have "their own" number, unrelated to the IBAN (and they don't even have the name of the holder).
Some have the name of the holder, but not the IBAN.
As said it depends on the issuer, I have an account at a bank that issues the Bancomat card with the IBAN number (and my name on it and you have to wait for the card by mail for replacement), have another two accounts in two different banks where you can go to the teller, and he/she fishes a new card from a drawer and "couples" it to your account, the card is "blank", no name, nor IBAN, just the card number.
Fineco is I believe third or fourth bank in size, the two largest ones should be Unicredit (which casually is the one from which I have the IBAN connected card) and Intesa san Paolo (which is one of the two I have the "unconnected" card from).
My current experience is with some 30 payments daily, or 200 per week.
I would say that (from memory and very roughly) what happens here:
American Express or other "real" credit card: 2-10
Other embossed numbers credit or debit cards: 25-30
Bancomat/PagoBancomat (some with IBAN, many without): 90-100
Not embossed number Visa/Mastercard (as said sometimes they are the same as the Bancomat ones): 40-50
Prepaid or similar (not embossed numbers): 20-50