Magnetic Field = Electromagnetic Field?

It all depends. In free space there would be no essential difference, if the fields are propagating waves. But when you have sources and boundaries I beleive such a thing would be very inconsistent

It is fair enough to say magnetic field=electromagnetic field provided that the magnetic field is constant in time, as we know that time-varying magnetic field generates electric field and vice versa.

Only for transverse electromagnetic wave that can be safely said.

In principle Magnetic Field it's relativistic phenomena of electric field
(it's an good and comprehensive model)

If you know the magnetic field in all the space & time
you also know about kinematics of the elements which
transmit it by that you can derive the full electric field (space& time)
this gives you electromagnetic field :)
(and of course it's vice versa )

Regards

Electromagnetic consists of both electric and magnetic fields. In other words, magnetic is only one part of EM.

That is known!

For a transverse electromagnetic field both electric and magnetic field co-exist. Their ratio is defined as characteristic impedance. In free space is 377ohms.

I don't think so. In tranverse electromagnetic wave, electric and magnetic field both exist, it's just that the component in in the propagation direction does not exist.

Is electromagnetic field really a specific kind of field? Or I prefer that Electromagnetic Field is consist of electric field and magnetic field.

think of a magnet it has a magnetic field directed from one pole to another. But this field is not-varying and has no electrtic field part.

But another example is a propageting wave it has two companents: electric field and magnetic field.

No, it is not correct. Magnetic field has only magnetic properties of a vector field. But electromagnetic field has Electrical and magnetical vector components which depend on each other. So they are quite different terms.