This is a question asked primarily regarding jazz standards, where many different interpretations of the same tune can become well known. Compared to classical scores or transcriptions of rock recordings, lead sheets for jazz tunes are often a “secondary source.” Just as people might tell the story of the boy who cried “Wolf” differently from one another, the same tune might be presented differently from one fake book to the next. How do you know which is the best version?
One way to think about lead sheets is as recipes. Two cookbooks might present different recipes for the same dish, but the basic idea and finished product remain the same. Just as chef can prepare the same recipe with different options, different levels of flavor or other variations as they see fit, so too the same tune can be played with simpler or more complex harmonies. An example of that is in these two versions of the standard “My Shining Hour.”
While the melodies are nearly identical, the chords vary considerably. In measures 7-8 and 23-24, the second example’s harmonies are more complex, while the first chart has more harmonic movement in measures 11-12. Still, there are certain signposts that both sets of chords have in common, such as the Bbm7 at measure 17 and many spots where the second chart’s chord is simply the hipper version of the first (Ebmaj7 compared to Eb for example.)
Listen to several different versions of the same tune; familiarize yourself with commonly played variations, understand the basic harmonic function of a chord progression and discern when the same thing is being said with different chords. Fluency and versatility will help you and those with whom you play sound good on any tune.