big fish vs big shot

big fish and big shot both are nouns.

Word	Noun	Adjective	Verb	Adverb
big fish	Yes	No	No	No
big shot	Yes	No	No	No

As nouns, big fish and big shot are synonyms defined as:

Other synonyms of big fish include big cheese, big deal, big enchilada, big gun, big wheel, head honcho.

big fish (noun)	big shot (noun)
an important influential person	an important influential person