Those were words by Kepler. It's Latin for 'wherever there is matter, there is geometry'. It goes to prove that the idea that geometry held the key to understanding physics has been around for a long time. The factoring out of one of the masses from the equation of motion (or the fact that you could talk about gravitation without without one of the masses not really being there, and the other being replaced by energy, as Genady suggested) is a subtle clue that geometry is at the core of gravity.
As to push or pull, I think you mean something about attractive vs repulsive forces perhaps? But then it's not about F=ma vs F=GmM/r².
F=ma is the definition of force. It's a definition, rather than an equation really.
F=GmM/r² is a law of force, and it has a very different content.
It's when we equate both, as @Janus illustrated,
ma=GmM/r²
that we do have an equation, ie, an equality to be solved. The mere F=ma cannot be solved. Definitions cannot be 'solved'.
Not all equalities are equations. This is a common misconception. There are definitions, identities, formulas and equations.
Definition: velocity=space/time
Identity: x²-y²=(x+y)(x-y)
Equation: x²-2x+1=0
Formula: (c1)²+(c2)²=h², where c1 and c2 are the catheti of a right rectangle and h is the hypotenuse of the same triangle
A definition is just a labeling, an identity is an algebraic equivalence that's always true, an equation is the expression of a hypothesis to be solved from its statement in the algebraic language, and a formula is an algebraic statement involving ideas that can be abstract, geometrical, etc.
There is a long tradition of calling physical laws, definitions (and perhaps formulas) all 'equations', which might be at the root of your confusion.