in truth vs really

in truth and really both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in truth	No	No	No	Yes
really	No	No	No	Yes

As adverbs, in truth and really are synonyms defined as:

in truth and really: in fact (used as intensifiers or sentence modifiers)

Other synonyms of in truth include truly.

in truth (adverb)	really (adverb)
in fact (used as intensifiers or sentence modifiers)	used to give emphasis
	in fact (used as intensifiers or sentence modifiers)
	in accordance with truth or fact or reality
	in actual fact