The everyday world of magnets is really all about those magnetic materials that can be magnetised to make permanent magnets. These are the magnets that stick on the fridge door and are used for door catches and all are made from steel with a high iron content. The steel is magnetic because the iron it contains is magnetic.
Permanent magnets can be contrasted with those materials which are attracted to magnets (and are therefore magnetic) but do not themselves retain any magnetism when the magnet is removed. These are temporary magnets.
For now, when we refer to a magnet, we really mean a permanent magnet.