GR describes a relationship between the geometry of spacetime and its content of matter. The geometry determines how things move. ("Matter tells spacetime how to curve, spacetime tells matter how to move"). In particular, it determines which curves in spacetime we can think of as describing non-accelerating motion. The equation that describes the relationship is called Einstein's equation.
SR describes a spacetime called Minkowski spacetime, which is completely unaffected by the matter it contains. It's still different from the Newtonian/Galilean spacetime, which has all the properties that we intuitively associate with space and time. There's a natural way to associate a coordinate system with each inertial observer in both of those spacetimes. The main difference is that in Minkowski spacetime, there's a finite speed c that's the same in all of those coordinate systems, while in Galilei spacetime, the only invariant speed is infinite. This has a number of weird consequences, including time dilation, length contraction and relativity of simultaneity.
Minkowski spacetime is one of the solutions of GR. It's actually a solution that describes a universe that's completely empty, with no matter at all. SR is a theory of matter (that doesn't affect the properties of spacetime) and motion in that particular spacetime.