What is the difference between flaming's …

Fleming's left-hand rule and Fleming's right-hand rule were originated by John Ambrose Fleming, in the late 19th century, as a simple way of working out the direction of motion in an electric motor, or the direction of electric current in an electric generator.

When current flows in a wire, and an external magnetic field is applied across that flow, the wire experiences a force perpendicular both to that field and to the direction of the current flow. A left hand can be held, as shown in the illustration, so as to represent three mutually orthogonal axes on the thumb, first finger and middle finger. Each finger is then assigned to a quantity (electric current, magnetic field and mechanical force). The right and left hand are used for generators and motors respectively

Students tend to be confused on when to use either one as both have the same things on each thumb, forefinger and middle finger! 

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. 

DISTINGUISHING BETWEEN THEM:

In an electric motor, the electric current and magnet field exist (which are the causes), and they lead to the force that creates the motion (which is the effect), and so the left hand rule is used.

In an electric generator, the motion and magnetic field exist (causes), and they lead to the creation of the electric current (effect), and so the right hand rule is used.