The term metropolitan area is used to define the city itself as well as the surrounding suburbs or other urban areas. The city of New York, for example, has a population of 8 million, but its metropolitan area includes many other cities around it: a total of about 20 million people in all.
Megalopolis is a term used to describe large cities that are so close to each other that they start growing together. Boswash, for example, is a megalopolis that reaches from Boston to Washington, D.C. New York, Philadelphia, and Baltimore also belong to this region, which more than 50 million people call their home.
Megacity is a word used to describe very large cities, mostly over 10 million people. Examples are Mexico City, São Paulo, Mumbai, and others. Most of them are in developing countries, where thousands of people migrate from the countryside to the cities every day.
The Boswash metropolitan area
Image: “Physical Features of North America map”, by Tom Patterson, via Wikimedia Commons, Licence: CC0 Public Domain
modified by Klaus Rosmanitz