For electromagnetic, the waves are propagating (oscillating electric and magnetic moving through space) and the coupling between receiver and transmitter is weak (ie. loading the receiver has no effect on the transmitter).
Both are governed by Maxwell's Equations. Sometimes you'll hear these referred to as "near field" and "far field" -- though those definitions are nebulous in terms of modeling the coupling.
http://www.digikey.com/product-search/en/inductors-coils-cho...
The near field systems rely on both coils being within about one radius of one another, and the coils are typically self resonant, but the smaller you make the coil, the higher it's self resonance, thus it's efficiency is lower. That's the issue with resonant near field coupling, the small devices like phones limit the coil size, and efficiency. Near field demo:
Seems like the difference is in how spatially localized the two are, and % magnetic power vs electric.
Presumably though there is probably some way to drive (or receive) the wireless charger in a dangerous way so you can microwave things from a distance :p