rf - What is the difference between electromagnetism and electromagnetic radiation?

In a previous question, I asked if having 2 coils of wire with electricity flowing from one to the other is RF, and they replied that it was not Radio Frequency. I was puzzled because I thought this was wireless transmission of a changing magnetic field, which thus was RF.

I thought the rate of the AC current oscillation was the frequency of the RF (so a 60 hertz AC input I thought would give me a 60 hertz RF signal). Well, I was told NOT.

I would like to know the difference between electromagnetic radiation and just a plain, changing electromagnetic field.