I dunno why but for some strange reason, I keep seeing the StuG III as a tank base fitted with an AT/AP (the snub cannon is AT too?) cannon in front.

That's because it basically is. It doesn't have a traversing turret. Personally, I've never seen a shortbarrel version before, but I haven't researched them much.

Yeah, I don't think I have ever seen a shortbarrel version either.

Edit: Well, according to the internet the short-barrel version is the StuG III Ausf A.

http://www.historyofwar.org/articles/weapons_StuG_III_Ausf_A.html

Everytime I see a Stug I want to play Company of Heroes

The modified drive sprocket, gunner's sight position and spoked idler wheel make this an Ausf B. Early StuG III models employed the short-barrel, lower velocity cannon as their intended role was infantry support (as with the PzKpfw IV early versions). Up-gunned models were introduced with the Ausf F in 1942, as enemy armor became a greater threat.

Half of the posts here are of, in fact, the orignal KwK 37 L/24 versions.

StuG deploy now!