It now clearly distinguishes the two notions of gravity.
*) I've taken to calling one of them the extrinsic, framative gravity, g@f,
where @f means relative to some chosen frame f. This g is also called
gravitational field strength. It tells you the acceleration of a freely
falling object, relative to the frame f. It also tells you the weight
of an object (freely falling or otherwise) via W@f = m g@f.
*) The other one is the intrinsic, universal δg. It is frame-independent.
The reason that it is frame-independent, and the reason that I write it
as δg (rather than g) is that it tells you how the gravitational field
strength /changes/ as you go from (say) the center of the earth to the
surface.
It took me about five rewrites to come up with a consistent set of
concepts and a consistent notation. It's not perfect, but IMHO it
is a substantial advance over what went before.