And a tool and die maker certainly has excellent skills and can probably make about any part, but one in just that profession doesn't necessarily understand how parts interact and function together. Can he fix a Webley revolver that is out of time? Can he fix a stock that is broken or time a S&W cylinder?
It all depends on how much machinining a gunsmith was taught at his/her school. We had two semesters but just about all of us took it throughout our program just to make tools, work on guns or make parts or because of other classes like blueprinting, custom revolver, custom pistol. It could also depend on the gunsmith's background. The best machinist in our class worked 17 years as a machinist before going to school. Naturally he was better than any of us BUT he should be. After all, he made parts (via a contractor) for NASA.
I admit I was only one of two to make my own barrel vise (guys with $$$ bought it) and I did make a receiver remover (to safely separate an action from an acraglass bedded stock). There were many other tools including a little jig to reassemble the magazine release to the trigger group on a Mini-14/30.
Would I trust a guy who never took machine shop or worked in a machine shop and just watched AGI videos? Probably not.