Gravitational Force & Acceleration: What's the Difference?

[ASidd]

Would I be correct in saying that gravitational force is the force of attraction between any two objects and has the following characteristics:
Attractive and the magnitude of the force is inversely proportional to square of distance between the two object
It is given by the formula F=GmM/r^2

On the other hand acceleration due to gravity deals with the effect of the gravitational force on a body. This effect is to accelerate a body according to Newton's second law and given by the formula a=GM/r^2

 

[PeterO]

Would I be correct in saying that gravitational force is the force of attraction between any two objects and has the following characteristics:
Attractive and the magnitude of the force is inversely proportional to square of distance between the two object
It is given by the formula F=GmM/r^2

On the other hand acceleration due to gravity deals with the effect of the gravitational force on a body. This effect is to accelerate a body according to Newton's second law and given by the formula a=GM/r^2

That seems reasonable.
That acceleration you have calculated/given is for the body of mass m
The acceleration of the other body is of course a=Gm/r^2

IF the bodies have very different masses the smaller body, of course, has the larger acceleration.
Like when you drop an apple here on the Earth. The apple, with small mass, has quite an acceleration [9.8 ms^-2 actually], while the large body [the Earth] has such a small acceleration that most people [all people?] don't even notice it.