Quads an Triangles in some ways are semantic distinctions and in some ways technical distinctions. When it comes to the MOD file (and most other simple object formats), A quad really is nothing more than two triangles seamed together by an edge. However: in advanced modelling apps (like 3ds Max) quad faces are a class (to use the programming context of the word "class") unto themselves, with separate methods (which sometimes are similar to those of distinct triangles).
(okay, technically object classes that have distinct methods for their quads are of a separate class from objects without quad-specific methods).
I'm fairly certain I remember how UVW mapping is stored by an object in 3ds Max - I know nothing behind the inner workings of blender, sadly :/
What I do know forces me to stress one particular point: in XYZ space (your typical 3d-space) a vertex can only have one location, its X,Y, and Z... However in UVW space, that same vertex can have N locations where N = number of faces said vertex is used in constructing (this upcoming example DOES get a tad more complicated when dealing with triangulation, but hold that thought): The corner of a cube can have a set 3 UVW coordinates. (with a triangulated cube, that number might be anywhere from 3 to 6, depending on how it triangulates).
this gets even MORE complicated when dealing with multiple mapping channels (think an array of 3 dimensional UVW spaces), but that falls out of the purview of what MOD files can do at this time.
Hope that helps rather than hinders :3