all of a sudden vs of a sudden

all of a sudden and of a sudden both are adverbs.

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

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

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

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