important person vs doer

important person and doer both are nouns.

Word	Noun	Adjective	Verb	Adverb
important person	Yes	No	No	No
doer	Yes	No	No	No

As nouns, doer is a hypernym of important person; that is, doer is a word with a broader meaning than important person:

important person: a person whose actions and opinions strongly influence the course of events
doer: a person who acts and gets things done

Other hypernyms of important person include actor, worker.

important person (noun)	doer (noun)
a person whose actions and opinions strongly influence the course of events	a person who acts and gets things done