Does it matter where I hit enemies when shooting?
Yes! Aim for the head (or head-analogues)!
One of the loading screen tips alludes to this directly, but there are half a dozen other clues that you get bonus damage depending on where you shoot - the equipment which "increases headshot damage by X%", for one, and the multiplayer kill achievement for another.
Perhaps most viscerally, scoring a solid headshot on a humanoid opponent will cause their helmet to explode in a brief fountain of gore.
So aim for the head!