There is no real clear cut border betwen what is a x-ray and what is a gamma ray. The convention is to use the word x-ray when talking abouyt high energy photons produced in interactions with electrons, for instance bremsstrahlung or by knocking out a electron from a inner orbital.
The word gamma ray is used to describe high energy photons produced by deexcitations in the nucleus or other subatomic processes like antimatter reactions etc.
So to answere your question, there isnt realy any physical process comon to both since the two words are used to described photons originating in different physical processes.