Q:

What is the difference between the blackness of a Black Hole and the blackness of a Black Body?

Light cannot escape the gravitational pull of the black hole and hence the 'black hole' is black.
Any object that is black in color, absorbs all wavelengths of light and reflects none. So it appears black.

Could someone explain the key difference between these two phenomena ?

A:

A black body is a system that does not reflect photons. A black body can only emit photons, which is often fabricated as a hot cavity with a small hole. A razor blade can also approximate a black body if the sharp edge is smaller than the wavelength of photons of interest and is at a temperature so short wavelength photons are not significantly present. A black body then has a small reflectivity relative to the emissivity $r(\lambda)~<<~\epsilon(\lambda)$ for wavelengths of interest. An ideal black body has zero reflectivity for all wavelengths.
A black hole absorbs anything, including photons that reach it. It has zero reflectivity. Even if a photon entering a black hole reaches a mirror that is right at the event horizon, since the mirror has $z~\rightarrow~\infty$ the photon is not reflected back. The black hole also interacts with the quantum vacuum, in that virtual quanta across the horizon becomes an entangled pair of a negative energy quanta entering the black hole and a positive energy quanta that escapes to "infinity." This is a bit of heuristic, but it helps us see that a black hole losses a bit of mass and that mass escapes. The low energy form of this is of course photons, which have zero mass gap. As a result a black hole is about the most ideal black body in the universe. 

