Electric/Magnetic Particles I am given to understand these two things:


*

*Electrons are "the result of", "the cause of", and "the" excitation in the electron field. (Sorry, couldn't come up with a more succinct way to sum up all things quantum)

*There exist magnetic fields and electric fields and they are separate things.

*Whilst these fields are separate, the electron has a magnetic field and an electric one. They interact and electric fields can generate magnetic fields and vice versa.

*The photon is "the result of", "the cause of", and "the" mutual excitation of the electric and magnetic fields in directions perpendicular to each other and the path of the photon.


Given all these statements, I am want to wonder:
Why is there not a particle asosciated with just the electric field or just the magnetic one? Or, are there two types of photons: one that is the electric field and generates the magnetic field, and one that is the magnetic field and generates the electric?
Notes: I am still only studying at Scottish "Higher" Level so ideally there will be no maths beyond calculus. Also, still quite new to the Physics Stack so there may be more appropriate tags, feel free to change them if it will help get this question to the right folks.
 A: There are no separate magnetic or electric fields, these are just two aspects of the electromagnetic field.
In electrostatics and electrodynamics we generally think of electrons, positrons and protons as sources of the electromagnetic field. This suggests a picture where particles are fundamental and the field as somehow derived. For example, in a universe with no particles there would be no fields.
In QFT, it is the field that is fundamental and the particles are seen, as already commented above, as excited states of the field.
Carlos Rovelli, a quantum gravity theorist, believes that all there is, is just fields upon fields (this hides a lot of philosophical nicieties under the carpet as to the meaning of what is understood by fundamental).
A: The basic (because it's written by me, and I hope you get a better one:) answer to your question is the Faraday Tensor 
Two observers, moving at velocities relative to each other, are going to measure different values for electric and magnetic fields. So electricity and magnetism are two variations of the same field. They are inextricably linked, as even without going to Special Relativity, you can see this demonstrated in the Maxwell wave equation, which describes the propagation of an electromagnetic wave.  
Both the electric field and the magnetic field "rely" on each other to maintain the wave.
A: Your confusion comes from mixing three frameworks described with different mathematical models.
Framework 1.
Classical physics where particles are  massive, can be modeled with classical mechanics and classical electrodynamics ( maxwell's equations). An electron  when first discovered, was called a particle with charge and assumed it has classical charged particle properties. 
Classical physics could not explain a number of phenomena, particularly black body radiation, the photoelectric effect , the spectra in the light from different atoms. 
Framework 2.
This forced the invention of quantum mechanics, first the simple Bohr model, and then strict theoretical equation , the Schrodinger one to start with, and then for special relativity consistency, the Dirac, the Klein Gordon and also a quantized maxwell equation for the photons.
Simple potential problems could fit the data  for two body situations, explaining the atomic spectra etc.
Framework 3.
As experiments on these new microscopic entities progressed, two body quantum mechanical calculations were shown to be inadequate, and quantum field theory was invented, in order to model the data and predict correctly new situations.
The standard model of particle physics is mathematically a field theoretical model which at the moment describes most particle data.
In this model there are these fundamental point particles, some with mass and some with mass 0(gluon, photon)

The field theory used assumes that for each of the particles in the table each point in four dimensional space is covered by a particle field , and the particles one measures in the laboratory are excitations on these fields described by creation and annihilation operators which mathematically act on the free particle solutions of framework 2 above. To signal the existence or disappearance of an electron for example, one has to use an operator: creation operator for appearance on the electron field and a destruction operator for disappearance, on the electron field.
Now to come to your question:

Why is there not a particle associated with just the electric field or just the magnetic one?

The electric and magnetic fields are classical fields of framework 1. As nature is continuous it can be shown that the classical fields emerge from the quantum mechanical fields in a long drawn field theoretical calculation. A higher level built on the quantum underlying level. Thus light is emergent from a large number of photons in a complicated mathematically consistent manner, but a photon is not light, in the sense that a building is made of bricks , but a brick is not a building.
