Quantum theory is called "quantum" because it is supposed to be about quanta - discrete spectrum of certain quantities which in classical theory have a continuous spectrum. But actually, quantum theory does not need to be about quanta at all, because many quantum quantities actually have a continuous spectrum.

If you think it's confusing, then you've seen nothing. Quantum mechanics is (or at least used to be) about Schrodinger equation, which is a quantum theory of electron....