No that is not the case. They are essentially different things. and it will allow me to explain in simple terms some really important physical facts that are not well understood

You see the inverse square law for the decrease in the forces gravity and electrostatic fields form point sources is due to the fact that we live in a largely three dimensional universe and the area over which the field is spread increases as the square of the distance from the source so the force decreases inversely as the square. if we lived in a universe with a different number of dimensions (or even approximately so) the fall off of the force would be different.

We do experience and can show that the effect of this reduced dimensionality is real and this will lead to the second part of this answer but I will extend the ideas of reduced dimensionality first.

The gravitational or electrostatic force from an infinite (or approximately an infinite) line source falls off just as the inverse of the distance and the gravitational or electrostatic force from an infinite plane source is constant this is because the field can only expand into one or zero dimensions as you move away from the source.

We experience this on the earth's surface because to us gravity is essentially a plane source of force and to a first approximation is constant over the few miles of vertical dstance within which we all live

This also works the other way if there were four spatial dimensions, forces would decrease as the inverse cube of distance and there would be no such thing as a stable orbit!

Now back to the distance travelled by an object accelerating in a constant (note well, constant as we experience on the earth's surface)gravitational field

a constant force produces a constant acceleration (as long as things don't move too fast of course) so for a given time a body has moved a particular distance and in another similar time period it will move that distance again ie twice the distance but in that second period it has also acelerated enough to cover twice the distance in the same time well do it does both and the distance travelled goes up as the square of the time (this of course is a direct square law not an inverse one!)

Thinking a bit more about this it means that the distance fallen a body free falling towards a gravitating body a long way away where the force increases as the square of the distance travels much further than a simple square law would imply because the acceleration is increasing as the body approaches the source this is why comets in long elliptical orbits take such a long time to come back but only spend a brief period close to the sun.