city center vs metropolis

city center

noun
  • The central business and shopping area of a city. 

metropolis

noun
  • A large, busy city, especially as the main city in an area or country or as distinguished from surrounding rural areas. 

  • The mother (founding) polis (city state) of a colony. 

  • The see of a metropolitan bishop, ranking above its suffragan diocesan bishops. 

  • A generic focus in the distribution of plants or animals. 

How often have the words city center and metropolis occurred in a corpus of books? (source: Google Ngram Viewer )