Adverbs. They basically refer to the same (synonyms) but, probably refers to an action that most likely will occur and possibly refers to an action that has a chance to happen.

Possibly: might happen, maybe 50% chance it will or it won't. Probably: most likely happen, more than 50% chance it will happen.

(lots of dark clouds in the sky) It will PROBABLY rain today. (a dark cloud in the distance) There's a small chance it will rain. Maybe. POSSIBLY it will rain.