Your questions touch on a fundamental (some would say the fundamental) problem in theoretical physics. The easiest way to understand the issue is to think about how the two theories describe the forces of nature.
The general theory of relativity is our best concept of gravity. It states that the presence of mass distorts the space-time grid, like a bowling ball that sits on a stretched rubber sheet. Particles then move in the shortest paths along that distorted grid, a process we interpret as the effects of gravity. Thus, relativity, in essence, gives a geometric interpretation of gravity.
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