This question looked so lonely. And I'll admit I looked things up on the internet to find an answer. I was surprised that they weren't the same thing. (Although it appears that the two phrases are occasionally interchanged; from a practical
standpoint, there is no misunderstanding if one phrase is substituted for the other.)
Inverse square law
: The intensity
of light falls off as the square of the distance from the observer. (also applicable to other radio waves, radiation, and I think sound, too.) This I suppose has applications theatrical lighting.
Law of Inverse Squares: (paraphrased from several citations) This applies to gravity in that the degree of attraction between two objects varies inversely with the square of the distance between their centers. In addition, the degree of repulsion (or attraction) between two like (or opposite) charged particles varies inversely with the square of the distance between the two. This phrase (in its application to gravity) is usually attributed to Isaac Newton and Robert Hooke. Later, Joseph Priestley showed that it applies to static electrical charges.
I suppose its an academic difference in the naming. The inverse square of the distance relation is common to both. A subtle difference is that the first applies to a point
source and an observer, and in the second, two objects interact with each other.