[geordief (OP)]

If a Field (are all Fields  fundamentally  similar?)  is a set of possible ordered measurements of an appropriate test object in Spacetime   ,is a Wave  simply a propagating disturbance of  this Field?

Specifically ,when we come to Electro-Magnetism  are there 2 distinct** Fields , the Electron Field and the Magnetic Field?

Is there (separately?) such a thing as an Electro-Magnetic Field? (I have seen this description referred to) Is it perhaps just a superposition of the two distinct ** Electro and Magnetic Fields?

**the 2 phenomena seem "joined at the hip" but perhaps their Fields are distinct....

[Colin2B]

I’m going to keep this simple, so a few shortcuts ok.

are all Fields  fundamentally  similar?

No. You can have scalar, vector or tensor (you can also have spinor but I don’t recommend you get into them yet).
A good eg of scalar is temperature field - just a number, no direction, whereas vector has scale and direction.
There are also 2  important divisions, non-relativistic (needs a medium to propagate in) and relativistic (no medium so far  detected)

If a Field  is a set of possible ordered measurements of an appropriate test object in Spacetime   ,is a Wave  simply a propagating disturbance of  this Field?

Yes. Take an example of a water wave. We can define the height field and this will vary as the wave passes. Same with a sound field, measure pressure variations.

Specifically ,when we come to Electro-Magnetism  are there 2 distinct Fields , the Electron Field and the Magnetic Field?

Electric Field and Magnetic Field. Both of these can be defined separately if the sources are static.
In relativity they are seen as the same thing but from different frames of reference.

Is there (separately?) such a thing as an Electro-Magnetic Field? (I have seen this description referred to) Is it perhaps just a superposition of the two distinct Electro and Magnetic Fields?

More or less. A combination of the 2 but resulting from moving charges.

As i said, keeping it simple.

[geordief (OP)]

There are also 2  important divisions, non-relativistic (needs a medium to propagate in) and relativistic (no medium so far detected)

Perhaps a trivial question but if a wave was traveling in a medium with a very low resistance to its passage would its mathematical treatment tend to approach that of a relativistic wave such as an em or gravitational wave?

(Not that I can think of any possible examples )

[jeffreyH]

The measurements at points in a vector field determine a potential. This is entirely distinct from the propagation of the force carrier for the field. It is related to the equations of motion for a test particle in the field.

[geordief (OP)]

The measurements at points in a vector field determine a potential. This is entirely distinct from the propagation of the force carrier for the field. It is related to the equations of motion for a test particle in the field.

(my bold) that is the same thing as the wave,perhaps?

[jeffreyH]

Yes, but as Alan has pointed out elsewhere the force carrier will self-propagate.

[geordief (OP)]

Yes, but as Alan has pointed out elsewhere the force carrier will self-propagate.

That's the photon? It is the propagating disturbance in the EM Field?