city vs metropolitan area

city

noun
  • The central business district; downtown. 

  • A large settlement, bigger than a town; sometimes with a specific legal definition, depending on the place. 

  • A settlement granted special status by royal charter or letters patent; traditionally, a settlement with a cathedral regardless of size. 

  • A large amount of something (used after the noun). 

metropolitan area

noun
  • An area of population usually with a central or core city and surrounding towns or suburbs. 

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