MAT = Material
MOR = Morph
MATMOR = Material + Morph or FULL character apply
INJ and REM = Inject and Remove (Poser 5+ only)

All of these can be either PZ2 or CM2 or LT2 files where normaly:
PZ2 = Pose files
CM2 = Camera files
LT2 = Light files

but all three use the same syntax in their script language and Poser will apply the paramiters occordingly.

The MAT, MOR, Pose started when DAZ produced the first Morph Inj/Rem character and we had no where to put all those buggers in Poser 4 and someone had hacked the Pose files and we also had no where to put those buggers either. Many of us hacked them even further and began changing our MAT and MOR files into Camera files (CM2 rather then PZ2) in order to keep the depth of the folder system managable and be able to find things when we needed them.

However there where many who did not stick to calling their Pose Files 'xxxxx.pz2' and their Material files 'xxxxMAT.pz2' and their Morph inject files 'xxxxxMOR.pz2' and their Full (both texture and morph together) files 'xxxxMATMOR.pz2'; some because they just didn't know the difference and some because they thought it simply 'cool to be different'.

With P5/P6/P7 there is now the Material Room and now the extention has changed to MT5/MT6 (MT7 ??)

Therefore the best for most to understand and not confuse would be to refer to:
Material files; those that Change The Materials on an object or character, as MAT files.
Morphing files; those that effect the Morph params of a character or object as MOR files.
Pose files; those that change a character's pose position as Pose files.
Material/Morph combo files; those that change a character's morph peramiters AND apply textures as MATMOR files.
Inject and Remove files; such as DAZ uses on Vicky1,2,3 and Mike1,2,3 and SP3, etc as INJ and REM files.

But that may be too complex for many to follow so if MOR file sounds more chiek to some for files that only apply textures or MAT file sounds more 'cool' then MATMOR for files that apply a complete character....then one can just call them whatever they want and the person on the recieving end can just raise an eyebrow when they click on it and get a Totally different result then they expected and wonder "how come this person posts files for others to use when they don't know what the files are....good thing they are not a programer at 'my' company!"