These two adverbs, which usually modify adjectives, have basically the same meaning—“to some degree, or in part” and can be used in exactly the same ways:
We are usually partly/partially right and partly/partially wrong.
Since they are adverbs, they can also be used to modify verbs, prepositional phrases, and sentences when appropriate:
I partly told the truth, partially not.
Debbie quit her job, partially because she wanted to go back to school.