It depends on where the term is being used.
In our armed forces, the best armorers are the functional equivalent of gunsmiths. This would include the Marine armourers who build rifles or the Army's Welding and Machine Operators who do the same. The Army doesn't have an armourer MOS like the Marines do. Both USA and the USMC have lower echelon armorers who, depending on the level they work at, are parts swappers with the higher the level of training and assignment, the more difficult the work they can do. A classmate of mine was recruited by the AMU and works on pistols for the AMU (AMU went to TSJC and Colorado School of Trades looking for recruits). Britain's REME trained armourers are similarly trained (they can operate lathes, mills, weld) and a good book is Peter Laidler's book on the No 4(T). He describes his apprenticeship in the REME and how he had to build a sniper rifle to demonstrate his eligibility to become an armourer.
In law enforcement, armorers are like the lower echelon military armorers in that they are just parts swappers. I did that for a spell but never rebarreled anything like a gunsmith.
In the civilian world, there is no standard for gunsmiths. Even if the person is school trained, no two gunsmithing schools are alike. The better schools teach machine operation, welding, and stockmaking as well as repair work. The quality of instruction varies. The quality of a school changes too depending on the cirriculum and the instructors. There are also shadetree mechanics/gunsmiths, joe hobby, gun plumbers who call themselves as gunsmiths. There are no standards and I have a friend who works as a gunsmith but has never learned to operate a lathe/milling machine. He works as an armorer for numerous law enforcement agencies too. Additionally, some gunsmiths specialize narrowly in the areas that they work: shotguns, rifles, handguns, custom builders, or even just engraving or finishing. Take your pick.
BTW, both Germany and Austria have four year gunsmithing schools where the students build an entire action from scratch. They're also taught to decorate (engrave, checker) at those schools. The Austrian school has two programs with the four year being gunsmithing and the five years one being a gun designer. I know the Russians and the Chinese both operate gun designer schools where students are taught the operation and the engineering principles of firearms. They have access to many designs that they can study. I happened to buy a copy of the Chinese manual which in itself is a copy of the Russian manual. Too bad I can't read it.