An electric current can produce a magnetic field, but a magnetic field can also produce electric current.
This is discovered by Michael Faraday and Joseph Henry independently in 1831.
Electromagnetism induction is the complementary phenomenon to electromagnetism. Besides producing a magnetic field from electricity, we can also produce electricity from a magnetic field.
The difference is that, a steady magnetic field is produced by a solenoid or wire carrying electric current. whereas in electromagnetic induction, it requires relative motion between the magnet and the coil to produce an induced current.
REMEMBER: in order for electromagnetic induction to happen, there must be a relative motion between the magnet and the coil to produce current. That is, either the magnet or the coil shall move relative to each other.