They're related, to make things more complicated, see Maxwell.
http://galileoandeinstein.physics.virginia.edu/more_stuff/Ma...
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
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:
Most modern PM's are actually much more resistant to RF induction than one from strong magnetic fields mainly due to the saturation of the RF spectrum over the past 2 or so decades coupled with a decline in high voltage power in populated areas (they are underground as well as farther from residential areas these days).
That said I have no idea if the field those things generate is strong enough to create any issue with PM's or similar devices (like the "jump start" internal defibrillator some people are getting these days).
I would think that these devices are quite safe, especially considering that you see wireless charging station in courtesy area's in lobbies and other public places without any warning signs.
But there are guidelines for certifying consumer electronics compatibility with medical devices is on that list.
http://pics.camarades.com/v/jacques/renewables/windmill/dscf...
See those laminates at the edges? They're 'open' for that same reason, that way the magnetic field goes through the coils rather than that it heats up the steel and generates waste heat.
(that's from a windmill I built, diameter is ~ 12").