at once vs right away

at once and right away both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at once	No	No	No	Yes
right away	No	No	No	Yes

As adverbs, at once and right away are synonyms defined as:

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

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

at once (adverb)	right away (adverb)
without delay or hesitation; with no time intervening	without delay or hesitation; with no time intervening
simultaneously	at once (usually modifies an undesirable occurrence)