Or the definition could be that a sabot is a caliber sized cup that holds a sub-caliber projectile that separates/drops off after leaving the barrel.
It allows lighter projectile which usually means a higher velocity. However, there are some major differences between the mechanics and physics of powder burners and pneumatics with the valves we use. Shooting lighter pellets will generally give higher velocities but at a certain point the valving gets wonky because the pressure, valve dwell time, internal valve springs, hammer weight all combine to be very inefficient if set up for regular pellets. A certain amount drag is actually needed in the bore to get a good pulse of air, the low friction plastic sabots seemed to leave the barrel to quickly and hence did not have good velocity after all, OR I had to adjust the pressure up so high it was very inefficient and consumed much more air per shot.
I have been shooting custom built big bore pneumatics since the mid-ninety's and I tried sabots several times trying to work out all the problems. To shoot them WELL, the gun has to be tuned to shoot only them is what I ended up at. And I never could get much accuracy compared with regular pellets or slugs.
Powder burners have the same problems with sabots and accuracy. Yes, they are used but I have found in my Holy Black muzzle loaders that the plastic belted shoot better than the sabot bullets, the sabots are bad about flyers when the cup does not separate cleanly off the projectile. In pneumatics, lower velocity launch and the slower spin from the slower rifling twist also complicates the sabots petals opening up so that drag pulls the cup off the back, A petal opening up late or not at all causes the shot to veer off sharply. I found that I had quite a few odd shaped holes in the paper targets where the sabot had stayed on the bullet and caused tumbling or other accuracy defeating aerodynamics. It should also be noted that the military does use some sabot rounds in tank killer rounds and some navel defense stuff like electromagnet hyper-velocity cannons but the engineering and cost is horrendous.
Note that there is a bit of pistol ammo that uses sabot but it too is know for poorer accuracy (but in real world defense situations, a pistol is a short range weapon so accuracy is a much littler consideration. How much accuracy does a defensive shooter need in a pistol? Are you / should you really be shooting at someone 50 yards away with a pistol? The legal defense for that could be questionable and I live in a right to defend yourself state.) I did hunt hogs and deer with pistols in the past and sabot handloads just did not have the accuracy I required for my honorable hunting ethics.
I hunt hogs exclusively with air rifles now so consistent accuracy is more important than a target shooter who might not like a flyer but can accept an occasional one, I found sabots are a cool idea but not currently field ready in my .45 rifles.