Does the nature of EM wave depend on the magnitude of acceleration of the charged particle?
The fact that accelerating charged particles emit electromagnetic radiation demonstrates one of the deepest aspects of electromagnetism.
Charged particles are “sources” for the electromagnetic field. This means, they create an electromagnetic field that is tied to them and that electromagnetic field propagates out. If a particle is sitting still (which is equivalent thanks to Special Relativity to a particle moving at a constant speed), the field will be a Coulomb field falling off like 1/r and be time-invariant. An accelerating charge causes the electromagnetic field to develop “kinks” and these kinks aren’t stationary and propagate out as electromagnetic radiation.
Basically, charged particles have streamers attached to them and if you give them a yank, the streamers will come off. Those separated streamers are the radiation. The energy in the radiation comes out of the force that is accelerating the particle.