There are a lot of pistols which you don't have to release the trigger all the way forward when firing. You don't have to on my Glocks, nor my Beretta 92fs. It's the same way on the M4/AR15 also. On the M4/AR15 series, it's resetting the disconnector. I don't know what it's called on the M9 or Glocks, other pistols, but it can improve your grouping significantly, as it's a part of follow-through.
Everyone shooting an AR15 should "ride the reset". The same with pistols, if you have that functionality...and I would guess that most do. Riding the reset on follow through is nothing more than obtaining a new sight picture after the round fires and only allowing the trigger to go forward to the reset point. Here's how you feel what I'm talking about and what to look for. (It's the same on pistols which allow this functionality).
For pistols:
Remove magazine, set aside. Ensure no round in chamber.
1. Place on fire (or in case of Glock, pull trigger).
2. (Muzzle in safe direction) Pull trigger
3. While holding trigger to the rear, rack the slide to the rear and let it go.
4. Slowly release the trigger forward. When you feel the click, stop. That's the reset and that's exactly where you want to stop each time while shooting.
For the AR15:
1. Remove magazine, ensure no round in chamber.
2. Pull charging handle to rear and let it go home.
3. Place weapon on semi.
4. (Muzzle in safe direction) Pull trigger and hold to the rear.
5. With finger still holding trigger to the rear, pull the charging handle to the rear with your non-firing hand and let it go home (don't ride it).
6. Slowly release trigger and allow it to go forward. When you hear the disconnector resetting/feel it resetting, stop. That's the entire distance you should be allowing the trigger to go forward each time you are shooting.
Riding the reset provides for cleaner trigger manipulation because it doesn't allow your trigger finger to bounce off the trigger upon recoil. It stops you from essentially "slapping" the trigger, which as we all know will ruin any attempt at marksmanship and cosistent accuracy. It also takes all "creep" out of the trigger, because all the "slack" is hereby removed when done correctly.
Just my .02. Don't ask if the same will work on 2 stage triggers, because I don't know.
-Recoil