on purpose vs deliberately

on purpose and deliberately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on purpose	No	No	No	Yes
deliberately	No	No	No	Yes

As adverbs, on purpose and deliberately are synonyms defined as:

Other synonyms of on purpose include advisedly, by choice, by design, designedly, intentionally, purposely.

on purpose (adverb)	deliberately (adverb)
with intention; in an intentional manner	with intention; in an intentional manner
	in a deliberate unhurried manner