Rory,
It looks like the front axles are the same but the part numbers for the rear, intermediate and rear, rear axles are off by one digit and one letter. RS-12611-NSFS-11-780 for the LMTV rear vs. RR-15611-NSFS-11-780 for the rear, rear on the MTVs.
Intermediate rears are completely different because of the driveline requirements.
Further, there are two intermediate, rears and two rear, rears listed in the ETM depending on the UOC ("used on code")
The internal parts I glanced at are all the same so it has to do with the housings.
Knowing the military, it might be as subtle as a hose bracket mounted pointing a different direction.
Here are the LMTV and MTV rear axle pages from the manual for comparison.