actually vs in reality

actually and in reality both are adverbs.

Word	Noun	Adjective	Verb	Adverb
actually	No	No	No	Yes
in reality	No	No	No	Yes

As adverbs, actually and in reality are synonyms defined as:

actually and in reality: used to imply that one would expect the fact to be the opposite of that stated; surprisingly

actually (adverb)	in reality (adverb)
used to imply that one would expect the fact to be the opposite of that stated; surprisingly	used to imply that one would expect the fact to be the opposite of that stated; surprisingly
in actual fact
as a sentence modifier to add slight emphasis; as a modifier to add slight emphasis
at present