There is two basic types of projectiles, besides shot, that you can shoot from a shotgun - rifled slugs and sabots.
A rifled slug is a round nosed "chunk of lead" that has rifling cast right into the slug itself and is shot from a smooth shotgun barrel. Most slug mfg's suggest using either a cylinder bore or improved cylinder choke (but that may vary by mfg) - so basically can be shot from any shotgun with a fairly open choke (I have shot 20 gauge rifled slugs in my "fixed choke" (modified) single shot without issue as an example).
The "rifling" cast into the slug causes it to spin "as if" it was shot from a rifled barrel - it is however, a relatively short range projectile. It doesn't spin "that well" and it's usually quite heavy, so drops rather quickly.
The second type is called a sabot. They started out essentially as a pistol bullet inside a plastic sabot (wrapper) - think of the shot cup that holds shot in a normal shot shell - the sabot "holds" the bullet until it clears the barrel, then falls away allowing the bullet to continue down range on it's own.
Some sabot's can be shot with nothing more than a "rifled choke" or an "extended" rifled choke - those were some of the early ones. As the Sabot's became more popular, displacing the slugs in many cases, the mfg's started "tweaking" their sabot's. The Sabot part has spin imparted on it by the rifling in choke tube (or the barrel in fully rifled barrel), spinning it at the twist rate of the rifling, which in turn spins the bullet to try and stabilize it in flight.
Some of the ones that will fly the best, travel the furthest and hit the hardest NEED a fully rifled shotgun barrel to impart enough "spin" - One of Hornady's products comes immediately to mind that states right on the box "fully rifled barrels only" (or something to that effect).
So the rifled slug, typically weighing an ounce (438 grains), because it's heavier will hit harder "at the short range" compared to a sabot which may be 380 grains as an example, BUT will not have the same range - the sabot, because it's more aerodynamic and stabilized better will fly further with enough retained energy to kill a deer.
I have seen both slugs and sabot's in both 2 3/4" and 3" loads - I haven't seen a 3 1/2" load and don't think I would want to pull the trigger on it anyhow - these things "thump hard" at both ends - you shoulder knows immediately that you didn't shoot a waterfowl load.
As to range, that's more of a personal thing.
A "typical" 3" 1oz rifled slug which leaves the muzzle at 1700'ish fps/2800 ft/lbs (Federal Truball) still has 800 ft/lbs at about 140 yards (and 800 ft/lbs gets tossed around as the minimum for deer). **while it had 2800 ft/lbs at the muzzle it's down to 2000 ft/lbs by the time it has gone 25 yards - sheds quickly.
Using Federal numbers again, their 383 grain Fusion Sabot also leaves the barrel at 1700'ish fps but only has 2450 ft/lbs - however, because of the better ballistics it's still packing 1900 ft/lbs @ 50 yards and just under 1400 ft/lbs @ 120 yards - so it loses it's energy slower even though it started with less.
If you plan on hunting with Sabot's for deer (in 12 or 20 gauge), you would be best served by getting a fully rifled barrel (available for just about every popular shotgun) and shooting the best sabot's you can find that shoot well from your set-up.
