Flemings left hand rule tells the mechanical force F , on a conductor carrying current I placed in a magnetic field B (perpendicular to the current flow direction).
F = I L X B
Thumb is Force, Forefinger B. Middle finger I .
This rule is applicable in case of motors to know the direction of rotation of the motor.
Flemings right hand rule is for knowing induced current :
This is used in case of generators. Current is induced in a coil or armature by movement of the coil in a magnetic field.
The direction of induced current is given by this rule. Thumb, Fore finger and middle finger represent the same quantities as in case of left hand rule.