Whats the difference between time changing electromagnetic field and electromagnetic waves?
The basic distinction here is between "field" and "wave". An EM wave is a radiation of power. That radiation contains an electric and a magnetic field content. Both fields are in phase and, together they have a ratio of 377 in a vacuum. Without the phase alignment or the correct amplitude ratio they don't travel very far but can (if the circumstances are favourable) form a coherent EM wave such as at about one wavelength distant from a correctly made radio antenna.

Why 377 ohms? 

Thats the impedance of free-space governed by the square root of the ratio of magnetic permeability to electric permeability: -



The term "electromagnetic field" is looser and could be used to mean or imply: -


EM wave (due to it time changing as per the question title)
Near fields around an antenna
The magnetic field caused by an electric field