man of the world vs doer

man of the world and doer both are nouns.

Word	Noun	Adjective	Verb	Adverb
man of the world	Yes	No	No	No
doer	Yes	No	No	No

As nouns, doer is a hypernym of man of the world; that is, doer is a word with a broader meaning than man of the world:

Other hypernyms of man of the world include actor, worker.

man of the world (noun)	doer (noun)
a worldly-wise person	a person who acts and gets things done