I was reading an article from the New York Times Archive called “Broadway Theatre” published on Feb. 19. 1856 about a show called “Herne, the Hunter”. Evidently the show did not go well since the author states that “neither the scenery nor the machinery worked well. … Large demands are made on the stage carpenter, and it will be one or two nights before everything can be expected to work with exact precision.” Later though, the author claims that the scenery is good, but that it needs to be better lit.
This predates the first version of IATSE, which was the Theatrical Workman’s Council (started in 1863). It also seems to predate commercial scene shops, most of which seem to have started opening around 1890, though I am sure that there were builders operating before that out of a small shop, just as there are individuals today doing the same.
We have Stage Carpenters today of course; they typically help during load in, and run and maintain a show. If it’s a tour, the carpenter would likely be a Show Carpenter or perhaps a Technical Supervisor. Depending on the venue, a theatre may have an IATSE crew, and the “head” would be the steward. This person generally manages crew – but doesn’t usually handle dealings with the client, so it’s a tricky separation.