right away vs like a shot

right away and like a shot both are adverbs.

Word	Noun	Adjective	Verb	Adverb
right away	No	No	No	Yes
like a shot	No	No	No	Yes

As adverbs, right away and like a shot are synonyms defined as:

right away and like a shot: without delay or hesitation; with no time intervening

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

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