The number on your tags is the M&M customer number. You can also find that one on your account statement (miles&more website -> mileage account in detail).

I am pretty sure that the numbers on the M&M, FTL, SEN and HON cards are not credit card numbers. So for those who use the M&M credit card, they need different numbers that actually link to a bank account.
In the end it doesn't matter much since all those numbers (M&M, FTL,.. credit card) will link to your Miles&More account. You can even credit miles to your temporary M&M number and still get them.
Correct me if I'm wrong. I don't have an M&M credit card.