I think the Turret numbers are really for identification within the unit and were painted on at unit level.
The factory identifying numbers are the only unique identifier for any particular Tiger, and these are stamped into the chassis, turret etc.
It is entirely possible for there to be more than one tank with the same turret number as different units may have used the same or similar numbering system. I believe one common system was:
1st number is the company the vehicle belongs to.
2nd number is the platoon the vehicle belongs to.
3rd number is the individual vehicle number.
Company HQ tanks often replaced the second number with a 0 and sometimes began vehicle numbering from 0.
So a companies numbering system might look like this:
HQ - 201, 202 (or 200, 201)
1st Platoon - 211, 212, 213, 214, 215
2nd Platoon - 221, 222, 223, 224, 225
3rd Platoon - 231, 232, 233, 234 ,235
4th Platoon - 241, 242, 243, 244, 245
This is a very simplified version of the general numbering system, and many different variations of this and other systems were used in practice.
Turret numbers get changed on specific vehicles too as they are transferred within a unit or between units. So it is also possible for a tiger to have more than one turret number during its lifetime.
Turret numbers are not a very accurate way to identify particular tigers, it is much better to try and match up unique features such has hit marks and battle damage, or production features.
