Yes. In addition, Special relativity says clocks moving faster through space tick slower than clocks that move more slowly. So let's say you're a GPS satellite

Yes. In addition, Special relativity says clocks moving faster through space tick slower than clocks that move more slowly. So let's say you're a GPS satellite. GR says your clock ticks too fast because you're farther from the center of the earth's gravity well than the wristwatches of people on the surface. But SR says your clock ticks slower than a wristwatch on the surface because you're whizzing through space at ~15,000 km/hour. Which is right? Both. And they do not exactly cancel each other out (in general). So both GR and SR have to be taken into account to make GPS satellites produce accurate locations and times.