The grain weight is strictly how much the bullet weighs. What you are interested is in foot-pounds of energy that bullet arrives at it's target with.
Let's say that I reload a batch of 38 special, using the universal 158 grain lead round nose cast bullet. In the first batch I load 3.1 grains of HP38 powder ( a great all around pistol powder). This load will generate 782 FPS muzzle velocity, and a load of 3.7 grains of HP38 will yeild a velocity of 834 FPS..as the velocity increases, the foot-pounds of energy increases and so the 'stopping power' of the round increases.
Now take the SAME 158 grain lead cast bullet and load it in a .357 mag case, with 5.0 grains of the same powder, HP38, and the muzzle velocity is NOW 1109 FPS, or approx 30% faster than the .38 special load. I do not have the foot-pounds chart in front of me but the yield is much more.
Same bullet.. just travelling faster and therefore imparting more kinetic energy to it's target.
Make sense??
When you are ammo shopping, look for the right type of bullet for the job, and the factory rating of FPS muzzle velocity.