big wheel vs big gun

big wheel and big gun both are nouns.

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

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

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

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