all of a sudden vs all at once

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

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

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

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