What is the difference between an electric and a magnetic field? This question is a consequence of another question of mine which is about spin.
Here is my spin question.
What is the difference between these two fields? How do they occur? Am I right if I say that a magnetic field is about photons (because they occur between N and S poles of a magnet) and an electric field is about electrons? How they are related?
Finally; when and why do we use the word "electromagnetism"?
 A: The magnetic field is a consequence of special relativity. If a charge does not move with respect to you, you see only an electric field $E$, but if you start moving with respect to the charge, of equivalently if the charge is moving with respect to you, you observe a magnetic field of order $\frac v{c^2}E$ (in S.I units), where $v$ is the velocity and $c$ the speed of light. For instance, charges moving along circles create a magnetic field.
This is why electricity and magnetism are entangled and that we speak about electromagnetism. These fields are more precisely related by the Maxwell's equations. 
Historically, special relativity was discovered to interprete the Lorentz transformation ruling these equations when the charges are in motion relatively to the observers. Maxwell also discovered that electromagnetism propagates at the speed of light, $c$. Today we understand this because photons are the bosons  of electromagnetism, which means that the electromagnetic interactions are carried by photons. The attraction between charges or the effects of a magnetic field are the consequences of exchanges of photons between matter particles. See this question for more about this particular point. 
References :


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*Classical electromagnetism and special relativity

*Maxwell's equations

*Lorentz transformation
A: Electric forces are attractive or repulsive forces between "charged objects", e.g. comb and dry hair after some friction. Charged objects are those that carry some nonzero electric charge $Q$. The lightest – and therefore easiest to move – charged particle is the electron so the surplus or deficit of electrons is the most typical reason why some objects are charged.
Magnetic forces are attractive or repulsive forces between magnets, like magnetized pieces of iron. The amount of "magnetic dipole" carried by a magnet is completely independent of its electric charge. They're as independent as the gravitational and electrostatic forces i.e. as independent as the mass and the charge of an object.
For centuries, these two forces were thought of as independent. Only a few centuries ago, due to Faraday and others, relationships between the electric and magnetic forces began to be uncovered. Magnets may be produced by coils – by electric charges moving in loops. They become indistinguishable from bar magnets. Similarly, moving magnets produce electric fields.
In the middle of the 19th century, because of these "mutual influences" between electricity and magnetism, a unified theory was gradually found. Because electricity and magnetism influence each other, we need to talk about a whole – electromagnetism or, to point out that magnetism is related to moving electric charges, electrodynamics (dynamics sort of means "motion" or "reasons for motion"). 
James Clerk Maxwell wrote the unified equations for electricity and magnetism which exhibited a near perfect symmetry between electricity and magnetism. They are two independent "siblings" but they affect one another and the inner mechanisms in them are analogous. Maxwell's theory also implied that there are electromagnetic waves – disturbances in space where the electric field goes up and down and so does the magnetic field which is excited by the electric one and vice versa. Moreover, he proved that light was a special example of the electromagnetic wave.
In the 20th century, it was realized that the existence of the other force follows from one force (e.g. magnetism followed from electricity) due to a symmetry between inertial observers who are moving relatively to each other, i.e. due to the Lorentz symmetry which underlies Einstein's special relativity. It was also found out that the electromagnetic waves may be thought of as collections of photons and that the exchange of the photon is the "reason" behind electric as well as magnetic forces.
So the photons are the messengers of electromagnetism – both electricity and magnetism. Electrons are the most important carriers of the electric charge which means that they're the most important particles that produce the electric and magnetic (when electrons are moving or spinning) fields. These fields arise and affect other pieces of matter (especially electrons) due to the "messenger role" of the photons. Photons are "units" of the electromagnetic waves.
