How are magnets and magnetic fields related?
Magnets generate magnetic fields. The field originates from the N pole of the magnet and terminates at the S pole.
Each atom in the magnet is assumed to be a tiny magnet with some magnetic moment. When they are so arranged in the crystal lattice of the solid that their magnetic moments add up, the magnet is formed.
Even magnetic fields can align the atoms of unmagntized ferromagnetic materials ( atoms with magnetic moment) along each other and thereby magnetize it and form a new magnetic sample.