all at once vs all of a sudden

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

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

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

all at once (adverb)	all of a sudden (adverb)
suddenly	suddenly
all at the same time	quickly and without warning; happening unexpectedly; on impulse; without premeditation