very important person vs high muckamuck

very important person and high muckamuck both are nouns.

Word	Noun	Adjective	Verb	Adverb
very important person	Yes	No	No	No
high muckamuck	Yes	No	No	No

As nouns, very important person and high muckamuck are synonyms defined as:

very important person and high muckamuck: an important or influential (and often overbearing) person

Other synonyms of very important person include dignitary, high-up, panjandrum, VIP.

very important person (noun)	high muckamuck (noun)
an important or influential (and often overbearing) person	an important or influential (and often overbearing) person