A permanent magnet, such as a bar magnet, produces its own magnetic field all the time. It keeps its magnetism and always has a north pole and a south pole. Only a few materials are magnetic: iron, steel, nickel and cobalt. Metals such as copper and aluminium are not.
An induced magnet is a piece of magnetic material that becomes a magnet only while it is in a magnetic field. An iron nail held next to a bar magnet becomes an induced magnet and can pick up paper clips. When the bar magnet is taken away, the nail loses most or all of its magnetism.
An induced magnet is always attracted to the magnet that induces it, because its nearest end becomes a pole that is opposite to the pole facing it. Only a permanent magnet can repel another magnet, so repulsion is the true test for a magnet.