differ vs fight like cat and dog

differ

verb
  • Not to have the same traits or characteristics; to be unalike or distinct. 

  • To have diverging opinions, disagree. 

  • To be separated in quantity. 

noun
  • A program that diffs, a diff. 

fight like cat and dog

verb
  • To fight frequently or irreconcilably. 

How often have the words differ and fight like cat and dog occurred in a corpus of books? (source: Google Ngram Viewer )