What is the relationship between the frequencies of radiation absorbed by a material and those emitted? I know that Planck's law tells us the spectral radiance, but how does this map to those frequencies absorbed? For example, a black material at room temperature is absorbing all visible light and emitting infrared; what is the relationship between these two?
As an aside, what is the origin of the term "black body", since many black bodies aren't black!? I imagine that early realizations of black bodies indeed had coatings of black material, and this is where the term came from, an I correct?