In BrE, that would be "Rainfall will continue into [the] autumn". Mind you, in the UK, rainfall is likely to continue into and through all four seasons!
They are different. The first means that it will keep raining in autumn. The second means that it will keep raining until autumn, and says nothing about what will happen during autumn.
I disagree slightly. "Into the fall" (autumn) would include some of autumn (perhaps only 1 day). If one wanted to include all of autumn, one could use "through autumn". The problem with subtleties in interpretation is they only work if the speaker and listener both agree on the meaning.
Raymott doesn't specify that it will continue throughout the fall, so, while I agree with your interpretation, I don't see that there is necessarily a distinction there.
I disagree slightly. "Into the fall" (autumn) would include some of autumn (perhaps only 1 day). If one wanted to include all of autumn, one could use "through autumn". The problem with subtleties in interpretation is they only work if the speaker and listener both agree on the meaning.
I don't think this is a subtlety at all. If the weather bureau said that rain will continue into autumn, and it didn't rain at all in autumn, most people would say that they got it wrong.