right away vs at once

right away and at once both are adverbs.

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

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

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

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

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