one day vs ultimately

one day

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

  • At some unspecified time in the future. 

  • At some unspecified time in the past. 

ultimately

adv
  • Indicating the most important action. 

  • Indicating the last item. 

  • Used to indicate the etymon at which a given etymological derivation terminates. 

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