to the contrary vs on the contrary

to the contrary and on the contrary both are adverbs.

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

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

Other synonyms of to the contrary include contrarily, contrariwise.

to the contrary (adverb)	on the contrary (adverb)
contrary to expectations	contrary to expectations