Pretty much, yes. I know I sat down and worked it all out ages ago as to which unit was for which VIN ranges of P38 (originally) and which versions superceded etc, so dug it out and it's below:
I collated all that info from a parts tree on one of the many websites that have them - For reference, VIN XA410482 was the GEMS/Thor changeover VIN...
It's all a bit of mess and craziness! But superceded part numbers seem to be backward compatible (I.E. a JFC102550 unit will work on anything all the way back to AWR1012 vehicles with the AC/front screen/front heated seats options)... but they're not forward compatible, at least pre/post XA411503 which is where the wiring modification was done to have the compressor relay in the fuse box, like the Thor models had as standard.
My general rule of thumb is that if it's an AWR1012/5051 then it will work ok in the older versions that didn't have the updated wiring, as it monitors the compressor output feed for a load, and will throw an error if it doesn't detect enough of a load (IE just driving a relay coil), so it isn't suitable for the later vehicles, and will throw the chequebook fault all the time. A JFCxxxxxx unit will run the later vehicles with the wiring upgrade, and relay in the fuse box. they will also run the earlier versions, as it looks like they kept the MOSFET that drives the compresor clutch directly in the earlier models (so it's capable of handling the current) but just wrote out of the firmware to throw a fault if it didn't detect enough load - so it wouldn't throw a wobbly when just turning on a relay.
The JFC units will run the older ones, because as I mentioned above, they kept the MOSFET, so they are capable of driving the compressor clutch, so won't burn out of anything silly like that.
To bring it back on - topic, as I've digressed a bit... with the OP having an '02 model - it would have come with JFC102550 from the factory, and if it's got the AWR5051 unit in it, then it WILL always throw a fault as it's expecting to drive the compressor clutch directly, rather than just a relay in the fuse box...