Special Relativity is an extension of Galilean/Newtonian mechanics (motion of projectiles and other objects) to the case where the object is travelling at speeds that are a fraction of the speed of light. It deals with non-accelerating frames of reference. Satelites need to use this to correct for time dilation effects, but tracking the trajectory of an arrow/etc. or a car/etc. travelling from one location to another then classical mechanics is sufficient.

General Relativity is an extension of Newtonian gravity. It is also an extension of Special Relativity to cover accelerating frames of reference. Satelites need to use this, as does tracking the orbit of Mercury. However, for the orbits of other planets and the moon, using Newtonian gravity is sufficient for a reasonable degree of accuracy, and is used for tracking things like equinoxes/solstices, full moons, etc..