Mass defined as m = F_net/a is called inertial mass. Mass defined as m = F_gravitation/g is called gravitational mass. Many physicists, starting with the Hungarian Baron von Eötvös, have done experiments to determine if the two kinds of mass are equal and if they are the same for all materials. Recent experiments have shown that if they are different, the difference is only one part in 10¹⁵! Furthermore, Einstein’s General Theory of Relativity explains that they are identical, and calls this fact the “Principle of Equivalence” between gravitation and acceleration. In other words, the laws of physics in an accelerating reference frame or a gravitating frame are indistinguishable. You can’t tell the difference between falling or being acted on by gravity.