Okay, fairly straightforward examples. So, fair enough.

Though my initial question of what mass is is still up for grabs... And/or what is the so-called "resistance to acceleration," and how does that resistance work?

IE, if you push something, it resists being accelerated. How? I'm just wondering what the actual mechanism of "resistance" is. I guess it has to do with the equal and opposite force rule. But I guess the question circles back to causation.

I mean, we understand from observation that if we push something, it pushes back with equal force. But do we know WHY it pushes back with equal force, or simply THAT it does?

Knowing THAT it does is all well and good and we can base equations on it and do math with it (happy days for the math folks!). But personally I think the interesting question is the "WHY."

IE, if I hit a large rock, it hits back rather painfully and doesn't move.
So, I guess the interesting question to me is why that energy gets reflected back at my fist, and not used to move/deform the rock I just hit? Whereas, if I hit a sheet of fairly wet clay, my fist would tend to move right through it deforming it and spewing some clay out the back side of the sheet?

Now maybe this is more of a question of tensile strength and shear than a question of mass. But the same question basically applies. Why doesn't a "mass" act more like the clay in the example above than the rock? Why does a mass resist acceleration, rather than embracing it? What is the quality that makes "mass" resist acceleration?

I'm still thinking it all comes back to that M=E/(C^2) expression. Which could be written equivalently as

M = E/(C^2)
or
M = (E*(T^2)) / (D^2)
or
M/(T^2) = E/(D^2)

IE, Mass is simply an expression of the energy in a system in an algebraic or possibly geometric relationship depending on how it's stated (of course then that asks the question what is energy, in the final analysis).

So, it somehow seems like a "force" is an external expression of energy doing work on a system, whereas "mass" is an expression of internal energy opposing outside forces (or they're really flip sides of the same coin; one is pressing from the outside of an object, the other is pressing from the inside of that object). It just seems slightly unclear as to how the mass or energy actually "opposes" outside action.

I guess I still go back to a geometic / beach ball example, where an outside force acts to compress the contents, thus squeezing energy into a tighter space, similar to "pressure" in mechanical systems. And the tighter the energy is compressed, the more "energy-pressure" or "mass" it exerts, resisting further pushing in a geometric fashion. Ostensibly in a gradient.

IE, the more you squeeze it, the tighter it's packing the same amount of energy into a smaller and smaller space, thus the energy per square or cubic unit increases to an equilibrium point, where the outside force can no longer push any harder. And eventually, if energy is being imparted into the system it becomes additional "mass" tipping the scale, and beginning to push with a greater outward force than the inward force.

Does this make sense?

I mean, can we think of "mass" as a geometric function of the "pressure" of energy in a given compressed area (I'd assume a sphere, sinec that seem to be the most stable structure we find)? Where the pressure pushing outward at the surface varies with the size of the circle/sphere? I think this is kind of what i was trying to say in a few of my posts. I just don't know if it makes sense? Now obviously there may be more ways than simple compression to get outward force (spinning an object creates centrifugal force, etc.). But is the basic premise somewhat valid? That as you decrease the volume in which the same energy is compressed, the "mass" per square or cubic unit would go up? I'd assume that the "mass" would be the internal "energy pressure" to maintain equilibrium at the surface of the object (neither compressing, nor expanding the volume of the object).