A magnet is an object that has a magnetic field.
A so-called permanent magnet is made of a ferromagnetic material. Such materials consist of atoms or molecules that have each have a magnetic field (resulting from the spin angular momentum of electrons within them), but objects composed of these materials have magnetic fields only to the extent that these microscopic magnetic fields are positioned to reinforce rather than cancel each other. The details of transition processes back and forth between reinforcing and cancelling orientations reflect the behavior of the material's magnetic domains, which are zones of mutually reinforcing molecules or atoms.
An electromagnet has a field produced by a current, typically through a loop or a coil of many turns; its field becomes insignificant when the current ceases.
Various materials (soft iron is a frequent example), when exposed to a magnetic field, direct and concentrate it, and consequently share many of the properties of permanent and electro- magnets. It is not usual to call them "induced magnets", but their behavior is often described as induced magnetism. Combinations of electromagnets with such materials, for the sake of this behavior, are often designed as a form of enhanced electromagnet.
A magnet is a magnetic dipole. That is not really a statement about "having two poles", but about the mathematical properties of its magnetic field, which are reflected in the "magnetic field lines" or "lines of force" that are so convincingly evoked in the accompanying image. The poles are not a pair of things on or inside the magnet, but rather, for the purposes of this article, the two areas on the surface that look as they do in the image. (That look is a consequence of the highest surface intensity of the magnetic field strength occurring there.)
Having standard system of naming the poles of magnets is important. A magnet can be regarded as having two magnetic poles, one "north" and one "south". Historically, those terms reflect awareness, by early scientific researchers into magnetism, of the relationship between magnets and the earth's magnetic field. The end of a freely suspended magnet that starts to point more or less towards the Earth's geographical North Pole, is called the magnetic south pole; correspondingly, the other end that ends up pointing south is the magnetic north pole. Using this approach as a definition of terminology for magnetic poles and fields would require a clarification about the terms not being interchanged when the earth's magnetic field undergoes its next reversal. Without addressing the details, a formal definition in terms of direction of current in an elctromagnet and a "right-hand rule" defines north and south for magnetic fields, without reference to the earth's geomagnetic field.
The mistaken idea of a magnetic pole as a thing rather than as a description of the orientation of a magnetic field invites the expectation that cutting a magnet in half should separate the two poles. There are theories involving the possibility of north and south magnetic monopoles, which could be mounted at the ends of, say, a wooden rod to produce a dipole magnet. This could indeed be cut to separate the monopoles. In contrast, all known magnets have dipole fields resulting from motion of electric charges without such monopoles, and separation of parts of such a magnet merely produces smaller magnets with weaker dipole fields, each with ends that we label north and south. Unless magnetic monopoles turn out to exist, we will never see a north pole without a south one, because in all the magnets that have been found of or made those are complementary directions rather than two separable things.
"Permanent" magnets can be demagnetized in the following ways:
Magnet is also the name of a commune in the Allier département, in France