once upon a time vs one day

once upon a time

adv
  • A long time ago; at some time in the past (a traditional beginning of children's stories, especially fairy tales). 

one day

adv
  • At some unspecified time in the past. 

  • At some unspecified time in the future. 

  • Used other than figuratively or idiomatically: see one, day. 

How often have the words once upon a time and one day occurred in a corpus of books? (source: Google Ngram Viewer )