I'd add a third category: General purpose/utility. It's the kind of gun that will work for everything; personal defense, pest control, all manner of hunting, and just blasting targets for fun.
In my opinion, there are very few guns that fill this role adequately. Yes, a short barreled HD gun can kill game, but the lack of choke tubes typical of such models is a handicap. Long barrel sporting guns can be used for HD, but the length makes them ungainly indoors.
What I would like to see are more guns that have a barrel of around 20" threaded for choke tubes that come optic-ready from the factory. None of that will revolutionize the world of shotguns, It's just an option I'd like to see more often.