I understand from context that both are different, but what rule applies here? Is there a general case where you change the word order and you change the meaning?
I will hopefully progress through high school
means that I hope (now) that I will progress through high school. On the other hand the statement
I will progress hopefully through high school
means that as I progress through high school I will be hopeful, most likely of achieving a high score that will give me entry into the university course I want.
We have to clarify one thing here.
is more like an imperative to me, though it does sound extraordinarily quaint. Progress hopefully is an awkward attempt to say something like I hope you'll make progress. but it's not a sentence I would want to use. I would simply say Make the best of it! and that's it.
can be applied in a sentence where there's a split infinitive. Once again, it still has a strange sound.