The idea of an adiabatic potential energy surface or adiabatic state is closely related to the Born-Oppenheimer approximation. This has been discussed on this site before in some detail. People frequently talk about diabatic states as well. It seems based on the reading I have done that a diabatic state is not really counter to an adiabatic state as one might expect from the names, but is sort of a different representation when looking at processes involving multiple potential energy surfaces.
So, my question is, how are adiabatic and diabatic states/surfaces/processes (what word should I be using here??) similar and how are they different? Can both pictures be used to describe the same processes all of the time or only some of the time (or perhaps I'm mistaken and they are never the same)?
Also, I think this is just terminology, but where does a nonadiabatic process fit into all this? I assume this just means there is a crossing of surfaces and the Born-Oppenheimer approximation breaks down, but that isn't quite the same as what I'm asking above I think.