make fun of vs parody

make fun of

verb

  • To tease, ridicule or make jokes about, generally in a pejorative manner. 

parody

verb

  • To make a parody of something. 

noun

  • A work or performance that imitates another work or performance with ridicule or irony. 

How often have the words make fun of and parody occurred in a corpus of books? (source: Google Ngram Viewer )