It's called arranging. Take a song and make it slower, faster, longer, shorter, a march, jazz, R&B, whatever style you want.
I have a friend, a jazz guitarist, who tells the story of being part of a band hired to play during a new product roll out for a heavy equipment company. It was requested that they play only one song... "For Your Eyes Only". They played it straight, jazzy, as a march, rhumba, mambo and Zydeco. Two hours of the same song in a number of styles. That's extreme arranging... on the fly.