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.