on a regular basis vs regularly

on a regular basis and regularly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on a regular basis	No	No	No	Yes
regularly	No	No	No	Yes

As adverbs, on a regular basis and regularly are synonyms defined as:

on a regular basis (adverb)	regularly (adverb)
in a regular manner	in a regular manner
	in a regular way without variation
	having a regular form