The Effect opposes the cause.
The south pole of the magnet is opposed by the induced south pole of the coil during the first case.
Lenz's Law:
Lenz's law is named after the German scientist H. F. E. Lenz in 1834. Lenz's law obeys Newton's third law of motion (i.e to every action there is always an equal and opposite reaction) and the conservation of energy (i.e energy may neither be created nor destroyed and therefore the sum of all the energies in the system is a constant).
Lenz's law is based on Faraday's law of induction. Lenz law states that when an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.
Lenz's Law should not be thought of as an independent law, because it is a consequence of the conservation of energy. The connection between energy conservation and induced emf is valid for any type of induced emf. In fact, the polarity of the induced emf as specified by the Lenz's law, ensures that the energy is conserved.
Lenz's law uses FRHR Fleming's Right Hand Rule which allows you to work out the direction of the current induced.
In order to apply either Right–Hand Rule to a moving negative charge, the velocity (v) of that charge must be reversed to apply the Right hand rule–– to represent the analogous conventional current.