It doesn't really "generate" a field. The EM field is always there, permeating the universe. An acceleting electron will _disturb_ the EM field (depositing some energy and momentum into it), and this disturbance will propagate through the field at the speed of light (naturally, since at the right energy level such a disturbance is what we call light). At high energies the disturbance will be finely localized in space and behave like a particle, which we call a photon. It's fine to refer to it as such also at lower energies, but slightly misleading because at the very low energies that we talk about here ("radio") it is very spread out in space and behaves more like a wave (with a wavelength of ~meters). In the case of AC, electrons are moving "back and forth" over a short distance (somewhat simplified but useful picture) with the same effect. Think about moving your hand up and down through water - you will create a wave.
Also, both E and M fields are required to transport any power using electricity. This is also true for DC current. See https://en.wikipedia.org/wiki/Poynting_vector - the formula multiplies E by B, therefore if any of the two is zero no power (or information) transmission can occur. This is true over the air, as well as over a wire.
Hmm sounds dangerously close to aether theory. I thought we had moved past this … that EM waves exist in their own right without need for a medium. Unlike sound say.
Aether refers to some historical ideas (which evolved over time), and though the word isn’t in use anymore the current model of fields has similarities (ofc in many ways very different). Have just been reading some of the history of this (Einstein plays a big role), it’s very interesting, thank you! :) You might be interested in this discussion https://news.ycombinator.com/item?id=27942970
Wilczek points out that field theories are aether theories — as is relativity.
“Aether just means this one particular historical model!” is branding more than reality; and hides the fact that modern theories also describe an everywhere substrate of which particles are localized excitations and gravity is localized warping.