world-wide vs cosmopolitan

world-wide is not a noun while cosmopolitan is a noun.

Word	Noun	Adjective	Verb	Adverb
world-wide	No	Yes	No	No
cosmopolitan	Yes	Yes	No	No

As adjectives, world-wide and cosmopolitan are synonyms defined as:

Other synonyms of world-wide include ecumenical, general, oecumenical, universal, worldwide.

world-wide (noun)	cosmopolitan (noun)
	a sophisticated person who has travelled in many countries

world-wide (adjective)	cosmopolitan (adjective)
of worldwide scope or applicability	growing or occurring in many parts of the world
spanning or extending throughout the entire world	composed of people from or at home in many parts of the world; especially not provincial in attitudes or interests
involving the entire earth; not limited or provincial in scope	of worldwide scope or applicability