at once vs immediately

at once and immediately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at once	No	No	No	Yes
immediately	No	No	No	Yes

As adverbs, at once and immediately are synonyms defined as:

at once and immediately: without delay or hesitation; with no time intervening

Other synonyms of at once include directly, forthwith, instantly, like a shot, now, right away, straight off, straightaway.

at once (adverb)	immediately (adverb)
without delay or hesitation; with no time intervening	without delay or hesitation; with no time intervening
simultaneously	near or close by
	bearing an immediate relation