Some people form bands which write and record songs to make money from it. When two or three singers sing the song it is called a duet or trio. Some people also make parodies of songs, which is usually changing the words of the song but keeping the tune. Parodies are usually made to make fun of a song or its writer/singer (parody artist "Weird Al" Yankovic is an example of this).
The word "song" is often used to describe any piece of music, even one without words or lyrics. The proper word for a piece of music without words is "instrumental".