I think you are right. Car's can be "Classics" of their Marque and I think it is "stealers" that allude to a car being classic long before they achieve any real status.
But a car that still looks almost like it popped out of the showroom a few days ago even after 20 years of existence makes a motor somewhat special in the mind of the owner.
I imagine the 40 year No-Tax & No-MOT on my steed will be long after I am gone. But that's OK.
The date was fixed last time I looked, rather than a period of time. Anything before 1976 or something like that? @brianp38dse might know. Think his Ford is tax exempt.