influential person vs high muckamuck

Other hyponyms of influential person include big cheese, big deal, big enchilada, big fish, big gun, big shot, big wheel, head honcho, celebrity, famous person, behemoth, colossus, giant, heavyweight, titan, elder statesman, eminence grise, Excellency, fixer, influence peddler, heavy hitter, hierarch, high-muck-a-muck, pooh-bah, kingmaker, bigwig, kingpin, top banana, magnifico, figure, name, public figure, nepotist, policy maker, power broker, powerbroker, sacred cow, sirdar, socialite, sun, dignitary, high-up, panjandrum, very important person, VIP, worthy.