in reality vs actually

in reality and actually both are adverbs.

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

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

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

in reality (adverb)	actually (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