on an irregular basis vs irregularly

on an irregular basis and irregularly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on an irregular basis	No	No	No	Yes
irregularly	No	No	No	Yes

As adverbs, on an irregular basis and irregularly are synonyms defined as:

on an irregular basis and irregularly: in an inconstant manner, not according to fixed rate or schedule

on an irregular basis (adverb)	irregularly (adverb)
in an inconstant manner, not according to fixed rate or schedule	in an inconstant manner, not according to fixed rate or schedule
	at an uneven rate
	having an irregular form