A) At the idea level, there are several different physical
phenomena of interest. Students need to learn about
these phenomena and these ideas.
B) At the terminology level, the same terminology is being
abused to describe different phenomena.
Ideas are primary and fundamental. Terminology is secondary.
1) Bad terminology will make problem (A) worse, but good terminology
will not solve problem (A), not by a long shot.
2) Making a fuss over the distinction of m/s^2 versus N/kg is
not sufficient to solve problem (B), let alone problem (A).
There is more to physics than dimensional analysis.
3) Since any quantity that scales like m/s^2 is will also
scale like N/kg, trying to draw a distinction between the
two requires misunderstanding the foundations of dimensional
analysis. Therefore I agree with the position Ludwik took.
The foundations are discussed at http://www.av8n.com/physics/dimensional-analysis.htm
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One can easily distinguish at least three different ideas that
are commonly misch-mashed together under the name "g". This
is discussed at http://www.av8n.com/physics/weight.htm
*) I-gravity is denoted gI and can be calculated using Newton’s
law of universal gravitation, as follows: It has magnitude
gI = G M / r^2 ........
*) L-gravity is denoted gL and is associated with the acceleration
of the laboratory reference frame. It can be measured by dropping
an object and measuring its freely-falling motion relative to the
laboratory. .......
*) E-gravity is denoted gE and is associated with the /total/
acceleration of the reference frame, relative to a nearby freely-
falling object. It does not distinguish among the possible
contributions to this acceleration, in accordance with the
equivalence principle. .........
For an observer at rest relative to the laboratory, gE is identical
to gL. For an observer in a car, using a reference frame attached
to the car, gE may differ significantly from gL. It will differ in
direction if the car is turning, and differ in magnitude if the car
is driving over the crest of a hill. ..........