"The scrunching up IS gravity" seems to imply that fairly adequately.

It was an interesting distinction IMO, because if you think about it a lot of confusion comes when people think about gravity as a discrete thing that actually exists, when in fact gravity is merely a description of the effects that come with spacetime curvature.

Since you answered: do you have a good way to visualize the curvature of spacetime? I really don't understand how to think about light-cones being distorted, because it's the curvature of a lorentzian manifold that stiches together light cones with distortion.

If you can only visualize curvature of a 2D surface (embedded in the 3D space), you have to imagine the space as being 1D. I don't know of any other way.