While the sun is a star, not all stars are considered suns. In order to be classified as a sun, any given star must have planets orbiting around it, and not all stars do. However, the sun is not the only star that has planets orbiting it.
In the early 1990s, astronomers discovered that there were planetary systems orbiting around other stars, essentially making them suns. While only a few were found at first, scientists now know that many such systems exist. These discovered planets are now referred to as exoplanets so that they aren't confused with the planets in this solar system.