"The acceleration of free fall" when doing kinematics
and "intensity of the earth's gravitational field as measured
by the acceleration of free fall" when doing dynamics,
accompanied by the change of units to N/kg.
The latter is a mouthful, but it allows you to repeat the point
many times.
I use the field point of view in introducing g. I use the symbol g to
represent the magnitude of the gravitational field and state that near
the surface of the earth, it has a value of 9.80 N/kg. I use the symbol
a_g (a with subscript g) to represent the acceleration of an object in
freefall near the surface of the earth and state that it has a magnitude