Milan is financially the most important city in Italy, and home to the Borsa Italiana stock exchange. It is the second most populous city proper in the country, but sits at the centre of Italy's largest urban and metropolitan area.
The Centro Storico is the historic centre of the city of Milan, contained within the area once delimited by the medieval city walls and today by the streets forming the Corso Navigli easily distinguishable on the map of the city.
Southern Milan is chiefly a residential part of Milan. While you can find a couple of old landmarks in here, there aren't as much of them as in the Centro Storico, and this part of the city is more "local" and "ordinary".