Shotgun:
The Shotgun in DUST is a Plasma weapon. It fires a number of small supper heated pellets of plasma. Initially the ammo pellets are held in electromagnetic suspension in the reaction chamber where they are supper heated until they reach a live plasma state. When the Shotgun is fired the plasma pellets are expelled by electromagnets in a process somewhat similar to how a Rail weapon works. (This is why both Plasma and Rail are calcified as Hybrid weapons.)

These superheated pellets contain an immense amount of energy in an unstable state. When they impact the target they release that heat energy, vaporizing the surface they impact, causing an explosive out-gassing of vaporized material. These projectiles are very deadly at close range, but as the pellets travel through the air they out-gas and cool, losing much of that stored energy. At 15m they impact like hot paint balls and by 25m they would have literally evaporated.

The reaction chamber and power packs used in the operation of the Shotgun make it one of the heaviest of the light weapons. This results in lower aiming/tracking speeds, as well as making it slow to bring to bare after a sprint. While the pistols can be aimed quickly, and the Infantry Riles are still fairly light to handle, the Shotgun is a ponderous thing for a light or medium suit to be carrying. Only the heavy weapons are slower to aim, and slower to bring to bare when coming out of a sprint.

The slower rate of fire of the Shotgun is a result of the time it takes to superheat the amo pellets into plasma.

Ion Pistol:
The Ion Pistol of course has a much smaller reaction chamber and smaller battery packs. For it to achieve the heat and damage potential comparable to a shotgun it requires an extended charge time, which in turn tends to overhead the pistol after a single charged shot. When not charged, the Ion Pistol shoots cooler plasma pellets which contain less heat energy and therefor do less damage.

Assault Rifle:
The Assault Rifle does not attempt to heat the plasma it fires to such a high degree, so uses a different reaction chamber configuration and smaller batteries. The Assault Rifle achieves its damage through a high rate of fire, while using cooler, lower damage, plasma. Since the plasma the Assault Rifle fires is cooler and denser, it does not degrade as quickly. This allows the Assault Rifle to achieve much greater ranges than other plasma weapons. There may also be other technologies used to assist in containing the plasma over such long ranges, but if so it is classified and I do not have access to it at this time.

Plasma Cannon:
The Plasma Cannon does not fire pellets. It super heats a 6" cylindrical rod into a fist sized ball of plasma which is expelled electromagnetically as a single flaming ball of bone searing ferry. While the surface of the ball out-gasses the same as a shotgun pellet, the shear volume of plasma in each shot insures that it retains massive damage potential over considerable distances. The massive heat buildup in the reaction chamber is expelled through a vent pipe that extends over the operators shoulder when the Plasma Cannon is fired. It is usually not a good idea to stand directly behind someone who is operating a Plasma Cannon as the blowback will toast marshmallows.