My naïve understanding is that you can model gravity as a force in a flat, static spacetime. Equivalently you can model gravity as a forceless distortion of curved spacetime. Both models can be translated faithfully into one another, so you can solve problems related to gravity in either domain.
My naive understanding is that forceless spacetime distortion predicts somewhat different things than the old model. That's how general relativity finally explained the procession of Mercury's orbit for example.
GP means that you can take the Einstein field equations (and their solutions) and use the metric tensors to map between flat and curved spacetime, with either way being equivalent. GP did not mean that those tools map from Newtonian flat spacetime to curved.
