Be that as it may, moving the goalpost aside. For me personally this fundamentally does matter. Programming is about giving instructions for a machine (or something mechanical) to follow. It matters a great deal to me that the machine reliably follows the instructions I give it. And compiler authors of the past have gone to great lengths to make their compilers produce robust (meaning deterministic) output, as have language authors tried to make their standards as rigorous (meaning minimize undefined behavior) as possible.

And for that matter, going back to the band saw analogy, a measure of a quality of a great band saw is, in fact, that the blade won’t snap in half in the middle of a cut. If a band saw manufacturer produces a band saw with a really low binomial p-value (meaning it is less deterministic/more stochastic) that is a pretty lousy band saw, and good carpenters will know to stay away from that brand of band saws.

To me this paints a picture of a distinction that does indeed have a difference. A pretty important difference for that matter.