Yes, the capital G in physics notation is generally used for the universal gravitational constant, 6.67 x 10^-11 Nm^2/kg^2. (And I remembered the numbers off the top of my head but had to look up the units. I'm out of practice.)
As for the mixed messages about g
, I think what it's saying is that the proper label for the standard gravity at the Earth's surface is g
-sub-0 or sub-n; but a g
(sometimes rendered "gee") is a unit of acceleration equal to the standard gravity, which is 9.8 m/s^2. If you're a jet pilot and you do maneuvers that subject you to an acceleration of 98 m/s^2, then you've experienced 10 g
of acceleration -- or you've pulled ten gees, more informally.