Faraday’s Law states that a changing Magnetic Field through a coil of wire will “induce” a Current in the wire, called an “induced current”.
The induced current is actually caused by an induced emf
The emf is generated by changing the Magnetic Flux, which is done by changing the magnetic field
Faraday’s Law gives the magnitude of the induced emf, while Lenz’s Law gives the direction.
For example: The motional emf for the metal bar on metal rails is: