How is Bragg's Law related to the Phenomenon of Diffraction? As far as I understand, bragg reflections is a geometric result which says that parallel x ray beams that are incident on atomic planes will constructively interfere at specific angles. Where does diffraction come in? Doesn't Braggs law exclusively deal with the case of light reflecting off atomic planes?
This, for example can be noted here:
"Why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence...This observation is an example of X-ray wave interference (Roentgenstrahlinterferenzen), commonly known as X-ray diffraction(XRD)." 
 A: I think it is because the Bragg planes are not continuous planes, on the length scale of a typical X ray wavelength. Rather each Bragg plane is an array of regularly spaced scattering centres. So the 'reflection' from a Bragg plane is the result of a discrete sum of terms, in which each term is the scattering from one atom or molecule. The individual atoms or molecules are thus causing diffraction. The total result combines some elements which are like the action of a diffraction grating, and some elements which are like the action of a stack of partially reflecting surfaces. 
When we consider reflection of visible light by a plane metal or dielectric surface, one is in the the regime where the scattering centres are closely spaced compared to the wavelength, so we choose not to use the word 'diffraction'.
In the end, then, I think you are correct that the terminology is somewhat a matter of human convention, but there is some reasonable sense to it.
A: X-ray diffraction in a crystal is due to superposition of the reflections from all of the planes formed by the molecules or atoms in the crystal. Those are the cleavage planes, and are also called the Bragg planes. For any given x-ray wavelength and any given spacing of the planes, there are only certain angles where the reflections are in phase with each other.  Those are the angles where the path length difference between a ray that reflects off one and a ray that reflects off the next plane is equal to one wavelength.  
From your question, it appears that you are thinking that each Bragg plane (each cleavage plane) acts as a mirror independently.  This is correct.  Also from your question it appears that you may be thinking that diffraction is a process that is distinct from reflection.  This is not quite correct.  
Descriptions of diffraction often involve thin transmission gratings and do not invoke reflection, but gratings can be reflection, transmission, or both.  A "Bragg grating" is a thick grating, consisting of stacks of parallel planes, each of which reflects a small fraction of incident light. Any set of parallel Bragg planes in a crystal is a Bragg grating. "Bragg diffraction" is our name for what a Bragg grating does to light. 
Interference is what happens when light waves having different phases are superimposed.  Diffraction is a name for interference, usually in the cases where the phase difference is due to the waves moving in different directions.  But "diffraction" and "interference" are the same physical phenomenon. In the case of Bragg diffraction, the superimposed beams reflecting from different Bragg planes in a parallel stack are parallel, so they are not moving in different directions, but we still call the results of their superposition "diffraction".
This article describes volume holographic gratings, whose Bragg planes affect light exactly the way that the Bragg planes in a crystal affect x-rays.
