It's the same as between "вероятно" and "возможно".

Probably means likely, little doubt. It will almost certainly happen. It is likely to happen. Maybe means almost the opposite. It might happen but it is not likely. It is unlikely to happen but it might. I will probably learn to speak another language if I work hard enough. I will maybe win the lottery.

I guess there's no big deviation between these two words.

Definitions OF Probably: adverb with considerable certainty; without much doubt Example: in all likelihood we are headed for war easy to believe on the basis of available evidence Example: he will probably win the election Definitions of Maybe: adverb by chance Example: we may possibly run into them at the concert|it may peradventure be thought that there never was such a time