If a magnetic field is just an electric field caused by Lorentz contracted charged particles ( https://the-educational-blog.quora.com/Why-does-electric-current-result-in-a-magnetic-field) then what is an electromagnetic wave?
In electrostatics, an electric field is observed after the separation of charges, e.g. between the two plates of a capacitor with an excess of electrons on one side. This is done by the help of a potential difference from an external source (for example from a chemical battery).
A magnetic field is observed after the alignment of the magnetic dipole moments of charges in a body. This is done by applying an external magnetic field.
In electrodynamics, one way of generating a magnetic field is to accelerate charges in a circle. For example, an electric current inside a coiled wire induces a magnetic field.
On the other hand, a magnet that is moved back and forth in a coil generates an alternating current in the wire.
then what is an electromagnetic wave?
Every charge under acceleration emits electromagnetic radiation: the electrons inside the filament in a light bulb emit EM radiation in the range of infrared and visible light, the electrons inside the coil in addition to the above described process also emit photons due to the acceleration in circles and for both examples in the case of an alternating current this radiation has an oscillating intensity.
Any EM radiation is called an EM wave, but this is a little bit misleading, because only for special cases you will be able to measure the oscillating intensity of a radiation, which is the case for radiation from AC sources and especially for radio waves.
Every EM radiation contains photons. (This is obvious when one considers that the source of EM radiation is always the excitation of subatomic particles and the relaxation with the associated emission of photons). The photon has an electric field and a magnetic field, both fields oscillate in a vacuum perpendicular to the direction of propagation (and both are perpendicular to each other).
So each EM radiation contains photons which propagate with wavelike components.