Personally, I couldn't tell you what particular pistol (or pistols) may be used by any instructor at any given moment.
Some makes/models may be used when an instructor may be supported by a major maker, or they may simply use what their students at any particular class are using (or required to use), and some may even have one, or more, "favorites" they rotate through using at one time or another.
As an instructor I need to be able to teach/train folks in using 1911's, TDA's (traditional double action, also known as DA/SA), some of the assorted DAO-ish variants ... and even DA/DAO revolvers.
Over the years I've often taken to choosing something from my safe that I know will be similar to what's being used by the folks with whom I'm working (as an instructor), or a similar issued weapon, or I'll simply use a handy weapon being used/carried by one of the people with whom I'm working.
I've often thought that far too much is made of whatever make/model/caliber some trainer may be using - and maybe distracting from the important aspects of the class content, to some degree.
Of course, some folks choose their apparel because it represents some sports team or other, or promotes their favorite brand of whatever, so I suppose it's inevitable that some gun enthusiasts want to emulate their favorite sport shooters & instructors by getting the same make/model/caliber of gun ...
At the end of the day it's safe handling & manipulation, and consistently controlled & accurate hits on the intended threat target(s).
Brand name of the particular gun? It's just a bullet-launcher.
Pick something of good quality made by one or another of the major makers, preferably made by one of them who have acquired a lot of experience in providing service weapons to LE/Gov users, and who offers good warranty support ... and even pick something in a nice color, if that floats your boat ... and then train, practice, train, practice & so on.
In instructor & instructor update classes, the attention of the instructors is usually focused on the targets, not the particular guns used to make good hits on the targets. They all work in the hands of a skilled user.
