Think of satellites and one immediately visualises large metallic devises which circle the Earth taking photos, analyzing and processing comprehensive data. These devices are called ‘satellites’ because they orbit the Earth and are dependent on its gravitational pull to maintain function in space. Since these are built on Earth and placed into orbit by humans, the term artificial satellite applies.
A natural satellite is simply a celestial body which orbits another. And these develop their orbital properties naturally. To maintain position in the solar system, the Earth rotates around the sun, making it a natural satellite of the sun. Likewise, the Moon depends on Earth for its place in the solar system and is its one and only natural satellite.