Treff was an action made by Meffert which has a horizontal block attached to the top strap which houses the strikers and coil springs. W. Müchler was a firearms merchant.
Yes, the actions are very similar but the side frame reinforcements are different and that may be attributed to the possibility that a different frame filer was sourced. Most have Greener safeties but one has a top strap safety. Considering that the Suhl-Zella/Mehlis area was one big gun shop, I'd say it is possible that about any craftsman could have contributed to the effort on the example and depending on the time constraint, all may have been sourced to different sub-contractor shops. Or the components on the examples could have been acquired from the same source and individual craftsmen added their own artistic flare making each slightly different. I don't know of a Suhl/Zella-Mehlis craftsman with the initials "ST" right off but I'll look. Any possibility that the "ST" is "S1", which is a forge mark or tube makers mark that crops up from time to time, many times on E. Schmidt & Habermann examples.
What it take to make a guess at the makers, etal.? Info on the initials on the tubes near the forend lug as well as just ahead of the flats. Also any stamps that are adjacent to the steel stamps. And a little time, of course.

Similar engraving as found on a DR??
Kind Regards,
Raimey
rse