I think the traditional scientific use is still future-oriented. The hypothesis-as-prediction is a forecast about the result of an implied, future test.

I'd argue that stats/probability folks pervert "prediction" by using it in contexts of mere information masking, stripping away the tense. There are many better words for this: speculate, extrapolate, estimate, infer, ...

I think in normal English of the public at large and lay people, "predict" and "forecast" have nearly the same meaning as speculation about a future outcome. The main difference is that we "predict" discrete outcomes while we "forecast" statistical outcomes.