From: All About Vision
A cornea transplant replaces diseased or scarred corneal tissue with healthy tissue from an organ donor.
A graft replaces central corneal tissue, damaged due to disease or eye injury, with healthy corneal tissue donated from a local eye bank. An unhealthy cornea affects your vision by scattering or distorting light and causing glare and blurred vision. A cornea transplant may be necessary to restore your functional vision.