What is the difference between electromagnetic field and electromagnetic radiation? What is the difference between electromagnetic field and electromagnetic radiation?
 A: Electromagnetic field is an entity that pervades all space. It may be constant in time, or change in time.
When this entity changes in time in a wavelike manner (for example, there is a field pattern propagating in more-less single direction), we talk about electromagnetic radiation, because the field pattern comes from specific direction, where there is some body producing it - the body radiates.
It is common to use the term electromagnetic radiation to refer to any time varying EM field that when propagating to infinity, its amplitude decays with distance from the source slowly enough: mathematically, decaying as function $1/(distance)^2$ (the Coulomb field) is not slow enough, so such field is not thought to manifest radiation, but decaying as function $1/distance$ is slow enough, so such field manifests electromagnetic radiation.
A: The electromagnetic field is a pair of vectors (or maybe some other mathematical construct) defined at every point in space.
Electromagnetic radiation is a phenomenon we observe in that field, when an excitation in the field propagates through it.
A: The electromagnetic field consists of electric field and magnetic field vectors whose cross product gives the speed  and direction in which the e m waves travel.But e m radiation is the power radiated by the field, which I think is calculated by cross products of electric and magnetic fields vectors giving what is called as the pointing vector.
