the TPMS has no additional hardware, just the ABS module comparing rotational speed of each tire to the other ones - less precise system, triggers warning at 20% relative difference and misses if all 4 tires are off equally...

the RDC system is using the radio senders in each rolling tire plus one in the spare, 4 antennas (rear right also picks up the spare tire signal), the whole thing reports to a dedicated RDC unit under the glove compartment - the system is very precise, reports 5% absolute deviation but very sensitive and gives a lot of false alarms... This system was used in E53 that were sold mostly overseas, not in the US - even though, you may find a unit or two still rolling in the US...

what is the label on the button on your center console (module A169) - does it say RDC or does it have a tire-flat symbol?