This issue has troubled me for many years, as it seems to have many of you.
Here is my 2cents.
g should be considered the "gravitational field strength". I happens to be
fairly uniform near the surface of this planet. Other planets have their own
value. I think, if we developed this idea more, the idea of E (elctric field
strength) would be easier to deal with. Charges accelerate when placed in a
E field. Masses accelerate in a g field. How neat an image! It is the wonder
of it all that all masses (if g only is present) will accelerate identically.
Since we often teach the kinematics before the dynamics, we find our selves
faced with the acceleration of 9.8m/s/s before we deal with g and feel the
need to call it g. There is our error. So, since I feel we have been asked
to vote:
g = gravity field strength
a sub g = acceleration of free fall
This has helped me firm up what I plan to do in the future, regardless of
what the text might say. The discussion of the discrepency, if noticed, will
be valuable.