irregularly vs on an irregular basis

irregularly and on an irregular basis both are adverbs.

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

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

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

irregularly (adverb)	on an irregular basis (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