city center vs downtown

city center

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

downtown

noun
  • The main business part of a city or town, usually located at or near its center. 

  • The human genitalia. 

  • heroin. 

adv
  • In or towards the central business district. 

  • Outside the three-point line, or generally far from the basket. 

adj
  • Of, relating to, or situated in the central business district 

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