When we smile genuinely, there are two major muscles that move. A Duchenne smile or Zygomatic smile involves contraction of both the zygomatic major muscle (which turns the corner of the lips up to meet the eyes) and the orbicularis oculi muscle (which raises the cheeks and forms crow's feet around the eyes). A non-Duchenne smile involves only the zygomatic major muscle and looks fake.
(Many researchers believe that Duchenne smiles indicate genuine spontaneous emotions since most people cannot voluntarily contract the outer portion of the orbicularis oculi muscle. As for the crow's feet, I prefer the term "laughter lines".)