The word “classical” has a standard meaning in the humanities, but not in science.
Ward Cheney and Will Light give a candid definition of “classical” in the scientific sense in the introduction to their book on approximation theory:
… the “classical” portion of approximation theory — understood to be the parts of the subject that were already in place when the authors were students.
There you have it: whatever was known when you were in school is classical. Yes, this definition is entirely relative. And it describes common usage pretty well.