The DMS tools uses the phrase 'firmware', when in general it actually means system files (except for when reflashing the box, when firmware really is updated then).
There are essentially 4 'components' to the DMS contents:
Firmware (a .pac file IIRC)
Headunit files (various files on PHTSYS)
System files (various files on PHTSYS)
Media (PHTDTA)
The key things that must match on the DMS once a box has it's firmware loaded, are the Headunit files. These are the things that obviously simulate the CD changer protocols between the phatbox and your headunit, and it's these that must match. Versions of the headunit files for a given 'firmware', it has been suggested, are largely irrelevant.
So in terms of the DMS Tools, 'Update firmware' really means 'Update all of the system files to this version', which includes everything required on PHTSYS, and it's the 'Reflash box' option that determines if the box firmware actually gets updated. So it sounds like the one DMS you have, already has your headunit files on there, whether or not that is true of the GM DMS is another matter, but there is an easy way to find out.
If you fire up the DMS Tools with the GM DMS in the cradle, and select 'DMS Tools' mode - once your DMS is selected, the 'firmware' dropdown should auto-populate with the appropraite manufacturer/version of firmware detected on the DMS.
If the 'manufacturer' of the firmware matches yours (ie VW, Volvo, Kenwood), that DMS is probably good to go. If the version (v1, v2, v3 etc) is different, you might want to consider 'Updating firmware' as I suggested before to get the versions the same. If you don't, you _may_ experience intermittent odd behaviour.
Hope that all makes sense!