big shot vs big wheel

big shot and big wheel both are nouns.

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

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

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

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