Analog systems rely on physics that tends to have «events» or discrete-like phenomena.

Digital systems rely on physics that have very analog bandwidths and finite rise times and tolerances.

Thus I vote that the essential differentiation lies in how it is convenient for us to analyze said systems. For a simple LRC filter of some size, it is usually not needed to think of single electrons, it is more convenient to analyze as a continuous system. For a ARM core, it makes sense to think of the multiply as a digital operation and not consider the rise time of the voltages going on under the hood.

Somewhat similarly, one might wonder if there truely are «stochastic» systems out there. (I believe that the physicists say «yes»). In many cases the system may well be deterministic, but it makes sense to analyze it as stochastic?