In physics there are two (and only two) kinds of energy: potential energy and kinetic energy.
Gravitational potential is the energy 'stored' in a unit mass, and depends on position, it has units of joules per kilogram. Gravitational potential energy has units of joules, so the conventional meaning is that these are different.
Gravitational energy is ambiguous: it depends on who defines what it is and how. Some authors equate gravitational potential and gravitational energy. This can be verified by reading say, a few dozen articles or textbooks. That is, there are more authoritative references than Tach at sciforums (but, you already knew that, didn't you?).
In short, IT DOESN"T MATTER what Tach thinks. It doesn't matter what anyone thinks they "should be", because energy is energy, and gravitational potential is energy per unit mass.
Not in the 'real good' theory of gravity. E/m = total energy per unit mass. And that quantity is a constant of the motion over every segment of the objects natural path. It has nothing to do with g along the natural path of the object. g has no effect on the natural path of an object. Gravitational energy is 'lousy' term for gravitational radiation. Gravitational radiation propagates the g-field. That's what they're trying to directly detect in the local proper frame of the CalTech gravitational wave experiment. There's plenty of indirect evidence for gravitational radiation. There is no gravitational radiation in Newton's theory. That was the dumbest argument and you think you won. The reason you have a requirement for gravitational potential and all the other stuff associated with acceleration and force is because Newton's model predicts the total energy at boundary is 0. The total energy of an object at boundary is 1 and it's a constant of natural motion. So is momentum and angular momentum. The object doesn't give up any energy to the g_field. It doesn't give up any energy or gain any energy along it's natural path 'to anything' since it's conserved over the natural path. After Einstein accepted that time and distance are relative he knew he was going to have to fix Newton's model. He did a great job that I'm pretty sure Newton would appreciate GR.
I actually provided you with details for the derivation of the relativistic energy equation. The one that predicts what the objects energy is at boundary. On a scale of 0-1 it's 1. Most of chapter 1 is about the derivation of the energy equation. I don't get it why Tach wants to argue about this stuff other than to troll you. You need to figure out how to evaluate the physics rather than counting on heuristic attempts to find some level of correspondence with GR and the publics Newtonian perception of gravity.