When it comes to describing Pilates, probably neither word applies, but classic would be the nearest thing.
Classical denotes reference to art and architecture (mainly) of Greek and Roman civilizations, and their modern re-creation. This give sense to terms like Classical Antiquity.
Classic is a term that is descriptive of an iconic, or one-of-a-kind book, movie, annual sporting event or car, for example.
While Pilates as a technique can be described as “a classic”, the term to describe it in terms of it’s original state (i.e., that which Joe P. invented) would be, appropriately, “authentic”, “pure”, or, even, “original”.
But, in the end, it’s all a game of semantics, and folks, by now, know what all of the above terms mean. Now if they could all agree upon the incontestable fact that the original method is the best!
Take it to the bank.