Rest mass can be thought of as the measure of energy that object posses. This mass that appears in Newton law of motion measures inertia and hence called inertial mass. Gravitational mass is like charge in coloumb law and tells us how much gravitational force one feels. Just like electrostatic force doesn't change depending on frames, gravitational force doesn't change even if one is moving. When object is at rest both inertial mass and gravitational mass becomes equal. Is it a mere coincidence. what does this implies?
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1$\begingroup$ See, Weinberg's soft graviton theorem: journals.aps.org/pr/abstract/10.1103/PhysRev.135.B1049 $\endgroup$– user87745Commented Jan 12, 2020 at 9:24
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No one knows for sure. The equivalence of gravitational mass and inertial mass is one of the two primary assumptions of general relativity from which the theory was later developed. The other is that the laws of physics are isotropically invariant. While general relativity has proven very successful in regions of low spacetime curvature and mass-energy concentration, it is postulated to fail in the vicinity of singularities like those at the center of black holes. If general relativity does break down in these regions and the laws of physics are the same throughout the universe, this suggests that gravitational mass does not inherently equal inertial mass, but that it nearly perfectly approximates it in low-energy regimes.
A more precise theory of gravity, presumably a theory of $\textit{quantum}$ gravity, would likely involve a disparity in gravitational mass and inertial mass that would reduce to equality in weak spacetime curvatures, yielding the predicted dynamics of general relativity.
