cry the blues vs grieve

cry the blues

verb
  • To complain, especially in order to obtain sympathy for one's own purportedly sad situation. 

  • To sing in the style of blues music. 

grieve

verb
  • To cause sorrow or distress to. 

  • To submit or file a grievance (about). 

  • To feel very sad about; to mourn; to sorrow for. 

  • To experience grief. 

noun
  • A manager or steward, e.g. of a farm. 

How often have the words cry the blues and grieve occurred in a corpus of books? (source: Google Ngram Viewer )