Seen most those designations before, and easily explainable.
I must assume the M , K and T are used in the normal context ( M , 3 door softtop; K, 5 door hardtop; T' stripped flatbed) . After that, the MK is a 3 door platform with hardtop fitted.
The MS eludes me, as it would be a 3 door platform with "S" for "Spezial" which translate to 'special purpose' or 'purpose-built' as my guess.
There were 716 K(urz) ( short). For a series of 716 with shorten wheelbase assault vehicles . There has been several videos bouncing around the web in the past. These also may be the MS's, as the K(urz) would be totally confusing with K for hardtop.
T weapon carrier ( or weapon platform) is a removeable body (platform) fitted to a flatbed ( T )
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The Trojan Horse... the 1st Pinz used to covertly carry troops into battle .
ATL Pinzgauer XM 718K TUM(HD) 6x6 FFR (aka The Green Grail)