be wrong vs mistake

be wrong

verb
  • To have an incorrect belief, to be mistaken about one's judgment or statement concerning something. (This entry is a translation hub.) 

mistake

verb
  • To understand wrongly, taking one thing or person for another. 

noun
  • An error; a blunder. 

  • A pitch which was intended to be pitched in a hard-to-hit location, but instead ends up in an easy-to-hit place. 

How often have the words be wrong and mistake occurred in a corpus of books? (source: Google Ngram Viewer )