A permanent magnet produces its own magnetic field all the time. It is made of a magnetic material, such as steel, that has been magnetised, and it keeps its magnetism. It always has a north pole and a south pole, and it can both attract and repel another magnet.
An induced magnet is a piece of magnetic material that becomes a magnet only while it is in a magnetic field. The magnetic materials you need to know are iron, steel, nickel and cobalt. Place an iron nail close to a permanent magnet and the nail becomes magnetic, so it can pick up paper clips. Take the permanent magnet away and the nail quickly loses most or all of its magnetism.
The pole that forms on the nearest end of an induced magnet is always the opposite of the pole that is close to it, so the induced magnet is always attracted and never repelled. A permanent magnet can attract an unmagnetised piece of iron, but it will never repel it. This is why repulsion is the only sure test that something is a permanent magnet.