The difference is that cosmo, meaning one , is just that one city in a city. And metro. meaning more than one, is just that many cities of one. Example Atlanta, Ga.=metropolitan /and a city in Atlanta, Ga.=Marietta
Cosmos means the universe where as the metro means the urban area.Therefore the words cosmopolitan and metropolitan convey a big difference in meaning .Cosmopolitan does not limit to a small area but it denotes the whole universe. Cosmopolitan is a very limited urban area.
Referring to a person, cosmopolitan means they are sophisticated. It can also refer to a company being international or broad-based or multi-ethnic. The term metropolitan refers to being a city or an urban area or a municipality.