First of all congrats for making FTL.
I don't know what you mean by Servicekartennummer but it is common that the numbers differ. Let's get startet:
The baggage tag show your M&M customer number ("Kundennummer"). IIRC it should contain 9 or 10 figures.
Your CC should have two different numbers: the normal CC card number starting with 5310 (16 figures) and your FTL number starting with 9922 (15 figures) below your name.
If you received a separate FTL card with your starter kit it'll have another FTL number (don't ask me why but it has been the case for quite some time now). All numbers are linked to your account. There is no need to request a new kit!