Magnetic field due to permanent magnets is the normal magnetic field.
Magnetic field due electricity flowing in conductors like a spiral wire, a loop of wire in the shape of circle or square - is magnetic field of induction.
A current carrying conductor loop or coil is moved through a magnetic field, or a magnetic is moved through a current carrying coil, electromagnetic induction occurs. An emf is induced across the conductor.
This induced EMF is in the direction such that, the magnetic field produced by it, counters the magnetic field which produced the emf.
When the magnet is moving left, for example, through a coil, a current in the coil is produced, such that, the magnetic field due to the current is in the right direction.