[Apache6]

Webstral:
Like you said, most shotguns can serve either function, and on many shotguns you can easily change barrels to make it more effective for other type of work.

Most 'duck' hunting shotguns have fairly long barrels (26 - 28" not being uncommon) and at least in the US are normally limited to 3 rounds (due to laws), though many shotguns can carry 5 rounds but use a 'limiter' (which is just a plastic piece that takes up space and can be removed during normal cleaning.

"modern" Home defense shotguns will likely have short barrels (18 - 20") and be pump or semi auto having five shot magazines.

Depending on who is likely to be defending against what, you might run into other calibers of weapons. I've given 3 female friends/relatives shotguns chambered for .410 shells, since they were both 'slight and relativey unfamiliar with weapons. In two of the three cases, the weapons were far more likley to be used against racoons but gave them peace of mind. In the third instance a friend had an ex who was 'stalking her.' We got her a pump action .410 shotgun and I made her go to the range five or six times over about a year. (We also got her a concealed carry license and a .38 revolver but thats irrelevent to your question.) It was not what I would chose to go into combat with, but it was the right weapon for her, my 12 ga Rem 870 was too big and kicked too much for her.

Most military tactical shotguns will have shorter barrels (18-20") larger magazines, and may be able to accept bayonets or lights. Shotguns are not used all that often by miltary (I think T2K plays makes them seem more effective at long range then they are)

During T2K era the USMC used remington 870s with 18 or 20 inch barrels and bayonet lugs, equipped with magazine extenders that let you carry 8 rounds (7 in tube, 1 in chamber IIRC). Some but not all of them had a collapsable stock. They were not a particularly common weapons, being used primarily for 'less lethal' situations. Combat Engineers and Recon Marines often had them for urban breaching operations (i.e. blowing either the locks or the hinges off of doors). These ones were more likely to have the collapsable stock as they were a mission specific 'secondary' weapon.