A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic). These include iron, nickel, cobalt, some rare earth metals and some of their alloys (e.g., Alnico), and some naturally occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic) materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism.
Some ferromagnetic materials can be magnetised by a magnetic field but do not tend to remain magnetised when the field is removed; these are termed soft. Permanent magnets are made from magnetically hard ferromagnetic materials that stay magnetized.
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. Often an electromagnet is wrapped around a core of ferromagnetic material like steel, which enhances the magnetic field produced by the coil.
The overall strength of a magnet is measured by its magnetic moment, while the local strength of the magnetism in a material is measured by its magnetization.
Data and images from http://en.wikipedia.org/wiki/Magnet