Hey Reb, fancy meeting you here! Yes there is a difference. The difference is the duration of the impulse. A shotgun's duration of recoil is longer therefore the perceived recoil is less, much like a muzzle loader. The lotal can be the same but the shorter the duration the sharper it feels. I can shoot a 10 gauge all day but my 454 Casull makes me act like Micheal Jackson on a dance floor. If an 18 wheeler bumps you at 2 miles per hour who cares right? but if a .177 pellet hits you at 1,000 ftps you'll howl like a girl right? (just kidding as usual) The real difference is the the perceived recoil. In the end a shotgun only spits it load at 1300 to 1500ftps and a bigger load compared to a 300 win mag. But the 300 spits out at a tiny load of 180 gr at 2800 ftps. All this is counter acted by recoil pads which delays the recoil impulse therefore delays the total recoil. Clear as mud? Not my fault!