on the contrary vs contrariwise

on the contrary and contrariwise both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on the contrary	No	No	No	Yes
contrariwise	No	No	No	Yes

As adverbs, on the contrary and contrariwise are synonyms defined as:

Other synonyms of on the contrary include contrarily, to the contrary.

on the contrary (adverb)	contrariwise (adverb)
contrary to expectations	contrary to expectations
	with the order reversed
	in a contrary disobedient manner