LEFT HAND RULE ( MOTOR): Essentially, the Left hand rule is used to figure out the motion resulted from the electromagnetism, in motor circuits (here, we have electric energy changed to kinetic energy). The Left Hand Rule is used when some information of the circuit is provided (current and magnetic field) and often you are required to find the direction of motion of force.

RIGHT HAND RULE (GENERATOR): The Right Hand rule is used in generator circuits where kinetic energy is changed to electric. Often you are given information on the magnetic field and a rotating wire (such as a dynamo or an electric generator) and you are required to find the direction of e.m.f. or the direction of (electric) current.