prep school vs private school

prep school

noun
  • A private or public school intended to prepare its students to get into prestigious universities. 

  • A private primary school which prepares its pupils for the common entrance examination most commonly at the age of thirteen, and subsequent entry into public school. 

private school

noun
  • A fee-charging private or independent school. 

How often have the words prep school and private school occurred in a corpus of books? (source: Google Ngram Viewer )