Only the last sentence is relative
Shot peening of (very hard and not at all formable) critical structural parts is done with very tiny steel shot at high velocity. The objective is to create those compressive stresses on the surface, similar to the stresses induced in tempered glass.
Grinding after shot peen tends to relieve these beneficial stresses through removal of material and heat, and introduces microscopic cracks and unwanted grinding stresses. Properly, there should be a heat cycle after grinding operations to remove the stresses produced by that process, but any such heat cycle would also remove the beneficial stresses from shot peening. On the other hand, shot peening can be used to relieve grinding stresses if a heat cycle is not possible due to metalergical (temper) requirements.
