The role of internal nuclear energy
What makes a planet different from a star is essentially the fact that a planet does not have any internal energy lasting billions of years. Such a durable source of energy can only be nuclear. So a planet is a body without any internal nuclear energy. Calculations show that thermonuclear reactions can only start at above approximately 13 Jupiter masses. Therefore, this value is the upper limit for the definition of a "planet".
Another difference between a star and a planet is the way they are formed. A star forms through the collapse of a gas cloud, whereas a planet forms, in general, through the condensation of silicate ("dust") and ice particles in a "protoplanetary" disk of various materials orbiting a star.
The two previous definitions lead to the same result : an exoplanet is a body with a mass of at most 13 Jupiter masses orbiting a star. However, there are exceptions to this coincidence.