this is just two ways of expressing Newton's law. What it says is the force on an object can be calculated by multiplying its mass times its acceleration, or tautologically, the mass of an object can be calculated by dividing the force on it by the acceleration it is experiencing. However, that object will still have mass if it is not accelerating.

Your statement "that mass is equal to force over acceleration" is completely wrong, and betrays a total lack of understanding of what force, mass and acceleration are, and what equations are for. Mass has NOTHING to do with force or acceleration. It is a property of matter, while acceleration is a mathematical relationship between space and time. Force is the relationship between the two, think of it as a form of bookeeping Newton invented in order to do his calculations.

If you need to convince yourself of this, consider a mass floating in space, not moving, not accelerating, with no forces acting on it. But it still has mass. Force and acceleration have nothing to do with its mass, its mass is what we can measure when we apply a force to it, but it was there all along. Or to put it another way, a mass in a gravitational field is accelerated, and we call the resulting force its "weight". A mass floating motionless in free space is weightless, but it still has a mass because it requires a force to accelerate it.

What the Newton's Law really tells you is that you can calculate the force acting on a mass by measuring its acceleration. Until you get that straight, the rest of your attempts to extend it to relativistic physics are just gibberish.