Or rather, if the magnitude of the EM wave is not of concern, then
what exactly is the information which is sent and what information is
received and decoded by the receiving antenna?
Let me give you some perspective on this, as it's a point that is often overlooked.
The whole reason you can receive a (weak, as you say) signal in the distance, is due to the massive redundancy of using an oscillating EM field, as opposed to, say, a single EM spike.
To give the idea in a super-simplified form, imagine a 1 MHz transmission as hammering on a telegraph key (EM "clicks") 1 million times a second, and then your buddy is listening to this and keeps the rythm with his left foot (he is very fast!). He knows the speed the beats should be coming with, and just tries to find the corresponding rythm.
Even if the signal is very weak and he misses say 80% of the beats, he can fill in the rest since he is keeping the rythm and knows where to listen.
So by deciding beforehand what rythm you and your buddy should communicate using, you can counteract the lossy medium and send a resilient signal (you could encode the message by slightly perturbing individual groups of beats backwards or forwards in time for example, this would correspond to FM radio then).
If someone else transmits on another frequency it doesn't affect your transmission as it would just drown in the rest of the noise the receiver hears.
Fortunately, you don't need to click on the telegraph key millions of times a second and find a buddy with a fast ear. In amazing convenience, nature provided us with the electrons, photons and metals. Depending on the actual frequency, you and your buddy are electrons spinning around atoms or flowing through a conductor, and the beats' best analogues are virtual photons, building up the transmitted photon.
This turned out a bit long-winded, but it's such a basic feature of physics and information that is often not appreciated.