On the F22/M235 there was a change very early in the production run, about March of 2014. That's why when you go to Tirerack, they ask if your car is pre/post 3/2014. I have an early 2014 (11/13 production) and I have the 'early' TPMS sensors. They are still 433MHz, but they changed vendors. From HUF (early) to VDO (later).
I have no idea what sensors fit various other BMW models, but you definitely need to match the sensors to the receivers in your car.
There are many third party sensors that are generic, and are programmed to the specific car model when the shop installs them. Easier to stock. In theory if you had one of these generic/universal sensors, you could reprogram them on the fly to do whatever you need them to do.
Something like these:
https://www.amazon.com/Autel-MX-Sens.../dp/B075SBSV5Y
You would also need the programmer tool. The Autel sensors above would use something like an Autel TS501 or TS601, like this:
https://www.amazon.com/Autel-MaxiTPM.../dp/B00BHCFNTS
I have the TS501, and it is a great tool. Really takes the guesswork out of dealing with TPMS sensors when you can query them directly. I originally got it to set the ECU on my sons FRS which requires an ECU reset/program when we swap winter/summer tires. That's common on most Japanese cars. No easy button press like on a BMW.
I used it a few weeks ago for a friend to prove out the sensors in his new winter tire set had not been programmed properly by Discount Tire. Made it easy for him go to back and specifically tell them what they goofed up on.
Before I coded pressure and temp in my iDrive display, I even used it as a quick way to check tire pressures. Just walk around the car and touch the tool to the tire and you get the pressure. No valve cap covers to mess with.