You are correct. The term "natural satellite" refers to any celestial body that orbits around another larger body. Moons are natural satellites, including Earth's Moon.
Many other moons exist in our solar system. For instance, Jupiter, the largest planet, has numerous moons, with the four largest known as the Galilean moons: Io, Europa, Ganymede, and Callisto. Saturn, Uranus, and Neptune also have significant numbers of moons. These moons are all natural satellites because they orbit their respective planets.
It's worth noting that some objects in the solar system, like asteroids or dwarf planets, can have moons as well. For instance, Pluto, which is classified as a dwarf planet, has multiple moons, including its largest moon Charon.
To clarify, the term "natural satellite" simply distinguishes these objects as distinct from human-made satellites, which are artificial objects placed into orbit around a celestial body by human technology.