[*Reserved*][1] means "tending to keep your feelings or thoughts private rather than showing them," while [*formal*][2] can mean "correct or conservative in style, and appropriate for official or serious situations or occasions." The words are related in that someone who is formal by nature or upbringing will also likely tend to be reserved. They are not ["true synonyms,"][3] however, in that they are not interchangeable but are related in terms of [*manners*][4] and [*comportment*][5]. See the linked definition of [*synonym*][6] at merriam-webster.com.


  [1]: http://dictionary.cambridge.org/us/dictionary/english/reserved
  [2]: http://www.macmillandictionary.com/us/dictionary/american/formal_1
  [3]: http://blog.dictionary.com/true-synonym/
  [4]: https://en.oxforddictionaries.com/definition/good_manners
  [5]: https://en.oxforddictionaries.com/definition/comportment
  [6]: https://www.merriam-webster.com/dictionary/synonym