What distinguishes the propagation of a gravitational wave from that of light (an electromagnetic wave)?

Answer

Light travels along geodesics, whereas a gravitational wave temporarily alters those very geodesics as it passes.

Light travels along geodesics (the straightest possible paths) in the local geometry, whereas a gravitational wave is a disturbance of spacetime itself that temporarily alters those very geodesics.

What distinguishes the propagation of a gravitational wave from that of light (an electromagnetic wave)?
propagationspacetimewavegravitational wave