Large damage to one body part.
I'm pretty sure this is the case, yeah - it fires a single high-damage projectile that looks like a swarm of pellets. To change this, one could go into the Weapons_Guns.xml in the Core/Def/ThingsDef_Misc files (in the mods folder) and change the damage from 1 bullet of 20 to some multiple of bullets adding up to 20... spoilering the rest due to space and all that:
<graphicData>
<texPath>Things/Projectile/Bullet_Shotgun</texPath>
<graphicClass>Graphic_Single</graphicClass>
</graphicData>
<projectile>
<damageDef>Bullet</damageDef>
<damageAmountBase>20</damageAmountBase>
<speed>55</speed>
[lots of lines I'm not fiddling with. . . . ]
<range>16</range>
<soundCast>ShotShotgun</soundCast>
to
<graphicData>
<texPath>Things/Projectile/Bullet_Small</texPath> [optional, depending on how you want the blasts to look. I find sticking with the existing shotgun blast graphics looks okay.]
<graphicClass>Graphic_Single</graphicClass>
</graphicData>
<projectile>
<damageDef>Bullet</damageDef>
<damageAmountBase>2</damageAmountBase>
<speed>55</speed>
[same bunch of lines I'm not fiddling with. . . . ]
<range>16</range>
<burstShotCount>10</burstShotCount>
<ticksBetweenBurstShots>0</ticksBetweenBurstShots>
<soundCast>ShotShotgun</soundCast>
Just tossed this together and tested it - it's not quite instantaneous enough for my tastes, but as far as kludgy tinkering goes it's not terrible. You might increase the net damage to get it to remain as effective, though - single, high damage hits seems to be the way to go in this game.
(I never tried combat realism, but considering how much hard & fancy work went into it I assume it had proper instant bursts.)
If you wanted it to be especially splashy in its bullet distribution, you could throw in the line <forcedMissRadius>2.4</forcedMissRadius> (taken from the minigun data) to ensure the bullets spread. Lowering that number from 2.4 to something like 1.2 should make it a little more likely to actually hit the target... in either case, using this will make it so that not many pellets will actually hit the target, but on the other hand will be more likely to hit whatever's nearby.
Doing a bit of further testing, 10 pellets of 4 damage without a forced miss radius gives the shotgun some pretty significant punch.
[Edit: Giving it a bit of thought, a single shotgun blast wounding everything from a person's leg to head seems a bit on the 'videogamey' side of things. Maybe if you shortened the barrel down to nothing or are using a blunderbuss, but the generic pump shotgun as depicted in the graphic for it would probably fire a tighter spread than that. Still, having some almost-guaranteed damage in every shot should give the shotgun some more utility.]