Intuitively, it seems to me that those examples of classical "non-determinism" are radically different from the quantum ones, in the sense that quantum physics theorize non-determinism, while those situations are merely "left out" by classical theory. (I'm not a physicist, if any one reads this, I'd like to know what they think :)

By "left out", I mean that there are multiple solutions to the equations of motion which are compatible with the initial values of the situation.

I guess this could also explain why there is such an association in this thread between non-determinism and non-predictability ?