In advanced physics circles, "classical mechanics" always means something very specific, and it doesn't mean "Newtonian." Classical means not quantum. Newton's theory of gravity is just one example of a classical theory. However, Einstein's general relativity is also a classical theory. Any theory which says gravitation is due to the exchange of gravitons would be a quantum theory. In this usage of the term, all theories are either classical or quantum. The quantum theories are the more fundamental ones, and the classical theories are in some sense approximations of them.

In advanced physics circles, "classical mechanics" always means something very specific, and it doesn't mean "Newtonian." Classical means not quantum. Newton's theory of gravity is just one example of a classical theory. Einstein's general relativity is also a classical theory. Any theory which says gravitation is due to the exchange of gravitons would be a quantum theory. In this usage of the term, all theories are either classical or quantum. The quantum theories are the more fundamental ones, and the classical theories are in some sense approximations of them.