The difference comes from the fact that the first statement—a statement of subjunctive possibility—says something about how things might have been under counterfactual conditions, whereas the second—a statement of epistemic possibility—says something about the relation between a particular outcome (a victory by Japan) and our knowledge about the actual world (since, as it happens, we know perfectly well that that particular outcome did not actually obtain, we know that what it says is false).
Consider the difference between the epistemic connection expressed by an indicative conditional and the causal or metaphysical relation expressed by a subjunctive conditional: The first statement says something that is certainly true, and will be accepted as such by anyone who is convinced that somebody shot Kennedy.
(Conspiracy theorists who think there was a back-up shooter, for instance, may accept the second statement.)
If one is told "It's possible that it is raining outside"—in the sense of epistemic possibility—then that would weigh on whether or not I take the umbrella.
But if one is told that "It's possible for it to rain outside"—in the sense of metaphysical possibility—then one is no better off for this bit of modal enlightenment.