As an armorer, I tend to call the assemblies by the terms used by the manufacturers of the various guns. It helps to use the correct nomenclature if ordering parts.
As a younger shooter, when learning to shoot pistols, I used the terms Slide Stop & Slide Release interchangeably, since both were commonly used terms for the same parts. Since I used my dominant hand thumb to quickly released a locked-back slide to run forward for chambering a round from the magazine, it didn't seem unusual to refer to the slide stop lever as a slide release, since it could perform both functions (locking and releasing a locked slide).
In subsequent years, as the semiauto pistol was replacing revolvers as LE duty weapons, I became a firearms instructor, and then an armorer for various brands of guns. The use of the support hand for performing the overhand and slingshot methods of releasing locked-back slides was becoming increasingly common. However, using the slide stop lever to release a lock-back slide was still a dominant method, especially among experienced shooters who used pistols with prominently sized slide stop lever tabs (1911's and S&W metal-framed pistols, to name a couple). The narrow, slim slide stop tabs, like those seen on the Glock and Walther 99's, was less easy to find and securely press to release a locked-back slide for
some shooters, and the overhand/slingshot method involving the use of the support hand was useful for such folks.
Like with many other manual manipulations of a gun, when there are a couple ways to perform some manipulation, different shooters may view advantages & disadvantages from different perspectives, including any previous training and their own experiences.
The overhand/slingshot method requires the use of both hands, and is usually a little slower when timed on the clock.
The use of the dominant hand's thumb used to press/lower the slide stop lever frees up the support hand sooner - to achieve a 2-handed shooting grip, or, to perform some other manipulation (especially during a defensive encounter), and gets the pistol back into battery and ready-to-fire condition faster, as well.
Trainers and experienced shooters have discussed the merits of both techniques for many years. One of the popular proposed advantages of the overhand method is that it's the same manipulative technique used for other purposes, like clearing some stoppages, Tap-rack-assess, etc, so it instills and reinforces the manipulation.
I've always been able to use the slide stop lever as a slide release, myself, even with the thinnest/slimmest of the lever tabs used on Glocks Walthers, SIGs, etc. As a firearms trainer I've seen it taught both ways, and have heard both methods discussed as being appropriate by different gun makers. I've listened to instructors discuss advantages and disadvantages of both methods for LH shooters using pistols designed for RH users (guns without ambi lever assemblies). As long as someone could perform either technique safely and effectively under stress, I didn't care which technique was used to safely get the gun back into ready-to-fire condition.
Just some thoughts.
