A magnet is a material or object that produces a magnetic field, which is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials like iron and attracts or repels other magnets.
A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An electromagnet is made from a coil of wire which acts as a magnet when an electric current passes through it, but stops being a magnet when the current stops.
Ferromagnetic materials can be divided into magnetically "soft" materials like annealed iron which can be magnetized but don't tend to stay magnetized, and magnetically "hard" materials, which do stay magnetized.
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