A permanent magnet produces its own magnetic field all the time. It has a north pole and a south pole, and it can attract or repel other magnets. Its poles do not depend on any other magnet being nearby.
An induced magnet is a piece of magnetic material, such as iron, that becomes a magnet only while it is in a magnetic field. When a permanent magnet is brought near an iron nail, the nail becomes magnetised and a pole is induced at each end. The end of the nail nearest the permanent magnet becomes the opposite pole, so it is always attracted.
This is why a magnet can pick up unmagnetised iron or steel objects, such as paper clips, but only another magnet can be repelled by it. Repulsion is the only test that proves an object is itself a permanent magnet. Most induced magnetism is lost when the permanent magnet is taken away.
