I think this got confusing because of a mix regarding the production of EM radiation/photons. There are a number of different processes that generate such, e.g.:
1) Annihilation; a particle/antiparticle annihilate and two photons are emitted.
2) An electron in an excited atom returns to a lower state and emits a photon
3) Moving charges generating EM radiation (e.g. radio)
pvinventor, regarding 3), the simplest analogy I can think of would be something like this; fasten one end of a string to a wall. Grab the other end with your hand. Move your hand up and down. Your hand will produce waves traveling along the string.
Your hand = an electrical charge (+ or -, doesn't matter) moving up and down
The string = the electromagnetic field
The waves = EM radiation (made up of "packets" called photons)
This is
basically http://www.allaboutcircuits.com/vol_2/chpt_1/6.html (but with no strings attached

).
mikelepore said:
Isn't it two photons, not one?
Pair production; needs only one photon (near a nucleus)
Annihilation; creates at least two photons.