There are 3 ways to intentionally cause the slide to go forward following a reload:
1) Slingshot - pinching the rear of the slide between thumb and forefinger, palm down, pulling it fully to the rear and releasing the slide, to go forward on its own power.
2) Overhand - palm of support hand on top rear of slide, thumb pointing to chest. Grasp the slide, pulling it fully to the rear and release the slide.
3) Slide stop activation - upon seating the loaded mag, a right handed shooter uses the left thumb to activate the slide stop while you are pushing the gun back out to the shooting position.
Many people say "slingshot" when they mean "over hand." Or maybe they don't. Regardless, the sling shot method is the least reliable. As far as serious use, the "slingshot" method doesn't belong in your tool set.
The Overhand method is reliable and nearly duplicates the actions used in clearing some jams. Learning one basic move to cover two different areas of gunhandling saves time to teach and learn while being easier to remember under stress.
The slide stop method is NOT difficult to do. Those that say you can't hit the slide stop under stress conveniently forget that you managed to find the mag release just fine, so it's really a non-issue as far as that argument goes.
The negatives for the slingshot and overhand method is two fold: 1) It does not take into account that if the gun has a Shok-buff installed, the slide may not be able to be pulled back far enough to disengage the slide stop. 2) It's slower for the first shot following the reload.
You can make sure that your guns don't have a Shok-Buff, but not one you may have to pick up that doesn't belong to to (say, a fallen cop's gun) that you have to end the fight with. Yes, that's a far-fetched scenario, so that leaves #2
The problem with the slide stop activation is that some guns don't have one. (Like a Walther PPK) or are so miniscule as to be pointless. (Most Glocks) For me, I won't be packing a PPK and my Glocks have the factory extended slide stop installed. Chances of having to do a "battlefield pickup" in real life is moot. The slide stop activation remains the faster way to do it.
That said, the wise learn BOTH the Overhand and Slidestop method. Sometimes, one works better than the other.