pooh-bah vs influential person

pooh-bah and influential person both are nouns.

Word	Noun	Adjective	Verb	Adverb
pooh-bah	Yes	No	No	No
influential person	Yes	No	No	No

As nouns, influential person is a hypernym of pooh-bah; that is, influential person is a word with a broader meaning than pooh-bah:

pooh-bah: an arrogant or conceited person of importance
influential person: a person whose actions and opinions strongly influence the course of events

Other hypernyms of pooh-bah include important person, personage.

pooh-bah (noun)	influential person (noun)
an arrogant or conceited person of importance	a person whose actions and opinions strongly influence the course of events