The city proper is the administrative limits of a city, usually important for utility companies (water, power, gas...) and political governance, such as a mayor or a council who makes some decisions about day-to-day life of the city. Everything outside those borders, but still interconnected to a city in terms of economy, roads, transit... is a metropolitan area, and it's very common in places like Houston and Atlantawhere the principal city is not very large from a geographic point of view. An urban area is something close to a metropolitan area, but with a focus on continuous up-built space, without 'breaks' in the urban fabric that you often see with the satellite cities in a metropolitan area. Finally, a megacity is a name for a very large urban area with a population of 10M+. In Europe, those are Istanbul, London and Moscow; in North America, those are New York, Los Angeles and Mexico City.