The first “Assault Gun” was the Sturmgeshutz III, a turretless fully tracked AFV with an armored superstructure and a short barreled 75MM gun and built on the Mark III and IV tank chassis. They were initially assigned to infantry formations as fire support and were part of the artillery arm rather than the Panzer troops. (their crews wore gray rather than black uniforms) Later in the war, the improved Sturmgeshutz IV and other similar designs were pressed into service in the Anti-tank role as tank killers, which they performed superbly.
http://en.wikipedia.org/wiki/Sturmgesch%C3%BCtz_IV
I’ve never seen this, but you are right. There is a big difference between a rifle and a gun.