Slug gun
Shortly after I was a kid, slug guns made their debut. In those days there were no saboted slugs only the hollow, weight-forward Foster slugs. The Brenneke slugs and sabots came later, as did rifled shotgun barrels. When I was a kid, the only sight(s) on a shotgun was the traditonal round bead near the muzzle. Then, some tests were done and it was discovered that the seemingly lack of accuracy associated with such guns and the Foster slugs was due to poor sighting with the bead-only.
Enter the paste-on sight. The first rudimentary attempt at improving a shotgun's accuracy was a short (under a foot), piece of stampted metal with a front sight and a rear sight that could be attached on the barrel, near the receiver with what amounted to as two sided sticky tape. It was not long after that when shotgun makers began to produce short barreled shotguns with both a front sight and a rear sight. The slug gun was born.
In short, a "slug gun" is a shotgun with features (short barrel, front and rear sights, maybe a scope, and nowadays, rifling), that make it dedicated to the shooting of slugs...nothing more, nothing less.