[SDC]

Yes, but because the surface area of transfer from the bullet to the target is so much smaller than the surface area of transfer from the gun to the shooter, it has a more severe (destructive) effect.
Some people will jump back when shot, as if the bullet was actually pushing them, but this is recognized to be a physiological response to pain, where the body is trying to throw itself clear (the same way that many people will involuntarily jump back if they touch something hot, or have a very bright light shone into their eyes). And, accounting for the slight loss of the bullet's energy while in flight, the energy transferred to the target would actually be slightly LESS than the energy felt by the shooter.