I think that if the circuit board was different on all key sets it would add an unnessary level of complication. It transmits a coded signal which was randomly chosen the last time it was inserted in the ignition and turned on. That coded signal remains unchanged and can be used to lock and unlock the car until the battery is dead.
Upon insertion in the ignition and the chip accepted it is given another random code to be used the next time it is needed to lock or unlock the car.
The chip in the fob gives the key all the security it needs, if the chip is the wrong one then the SKREEM will not react to the wrong signal even if the physical key has been changed to allow the ignition to be turned on. Change the chip to the correct one and all should be okeydokey. There is a sort of pun there.
That’s how I basically understand the workings. The circuit board is just a simple transceiver, sending a previously received coded signal and receiving a new coded signal to replace the old signal when sent.