The Special (as in Limited) Theory of Relativity, is a simplification of the General Theory of Relativity.
Essentially, if you eliminate acceleration, and any significant mass from the General Theory, you get the Special Theory.
Evidence for Special Relativity (solar moons for example), is also evidence for the General Theory. The General Theory is supported by:
- Universal expansion
- the spin down of binary pulsars
- frame dragging
- gravitational lensing
- gravitational time dilation