Assuming factory bought ammo...
Comparing your one question to the two types....
It can and can not.
Same barrel with two different bullets as you say, is really two different cartridges with different bullets.
Assume you can get both equal weights FMJ to HP.
same weight, same power, same manufacturer, same brass, same COL the HP will generate more pressure because the base of the bullet will be seated deeper in the case.
In reality you'll be hard pressed to find all things equal unless your a reloaded.
So heavier FMJ or Lighter HP.
It comes down to pressure and speed.
Slower FPS is easier on the gun and hand, but it really is a non issue on a modern handgun staying in SAMMI specs.
Get what you can store bought and unless your shooting 8k out of it or running rounds dropped in sand and mud through it you'll never see a difference between the two.