completion vs finishing touch

completion

noun
  • The act or state of being or making something complete; conclusion, accomplishment. 

  • The space resulting from such an act. 

  • The conclusion of an act of conveyancing concerning the sale of a property. 

  • The act of making a metric space complete by adding points. 

  • A forward pass that is successfully caught by the intended receiver. 

finishing touch

noun
  • A final addition, change, or embellishment that serves to complete something. 

How often have the words completion and finishing touch occurred in a corpus of books? (source: Google Ngram Viewer )