of a sudden vs suddenly

of a sudden and suddenly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
of a sudden	No	No	No	Yes
suddenly	No	No	No	Yes

As adverbs, of a sudden and suddenly are synonyms defined as:

Other synonyms of of a sudden include abruptly, all of a sudden, dead, on the spur of the moment, short.

of a sudden (adverb)	suddenly (adverb)
quickly and without warning; happening unexpectedly; on impulse; without premeditation	quickly and without warning; happening unexpectedly; on impulse; without premeditation