To make it more complex..
Megacity = City with more than ten million inhabitants.
Metropolis = Large, often western city which plays a significant role in part of the world with regards to economy, politics and culture. E.g.: London, New York and Tokyo.
Capital city = Most important city in a country usually housing the government.
Primate city = A city that, based on the number of inhabitants and its
functions, is much larger and more important than the second city in the country.