I believe that It was still classed as a tank, but its role leaned far more towards direct fire support for infantry against fortifications or other targets that held up the troopers - as opposed to an anti-tank role with. If I'm not mistaken, a self-propelled gun - in the US at least - was considered an artillery piece mounted on a chassis rather than towed. I say at least in the US because many classify the Stug as a SPG, though I classify it as an assault weapon; in many ways similar to the 105mm armed Sherman. Because the 105 on the Sherman didn't have that high of an elevation angle, it really isn't a SPG. However, that doesn't mean it couldn't be used as an artillery piece. Many M10s were set at angles and just fired their 3in (76.2mm) guns. Its definetly conceivable for a Sherman crew to do the same.
As for markings, I'm looking for some myself - other than the Tamiya provided decals. I personally wanted to know what units specifically they were used in and when. I was thinking of putting a Cullin device on it.
EDIT - Looking at my decal instructions on my Tamiya model, it provides for three tanks: one is a splotchy whitewashed tank from H Co., 69th Tank Battalion (Bttn), 6th Armored Division, December 1944 Ardenne; 48th Tank Bttn., 14th AD, 7th Army, January 1945, France; and H Co., 756th Tank Bttn., February 1944 Germ....

...yeah...

...wait....we..weren't..in..Germany in 1944 let alone February...LADIES AND GENTELMEN, WE HAVE A TYPO, TSK, TSK, SHAME ON TAMIYA. I'm still trying to figure that one out, I think it's supposed to be 1945.