We could get all philosophical here if we are not careful. Personally, I believe that if the relevant people at the time believed that a particular assemblage of parts was a particular locomotive, then thats what it was.
Main line railway companies had this 'problem'. The most efficient way to do major maintenance on steam locos was to tear them down to their parts, feed the parts into separate reconditioning systems, and eventually re-assemble a locomotive from the parts that were to hand. To a degree this was because reconditioning times were different for, say, boilers and wheels, which were different from times for cylinders and motion.
The Ffestiniog and Highland Railway, for example, now has interchangeable four wheel power bogies which will fit all the Double Fairlie and Single Fairlie engines, while the 2-6-2 bogies will fit all the Garratts (with the exception of the prototype K1). There are extra Garrattts in store should they be needed and only money and lack of need prevent more Fairlies being built. As with the Colt revolver and the Model T Ford, Yankee standardisation has its advantages.