The iPhone offers a digital music player to listen to your favorite music wherever you are. Once your music session is over, it's no use looking for a "Stop" button, as there is none. Indeed, the only way to stop the music on an iPhone is to tap on the Pause button and then on the Home button to return to the Homescreen. The iPod app will keep running in the background and after some period of inactivity, iOS will automatically close it.
You can also stop the music using the microphone button of the iPhone's headset.
You can also ask Siri (the voice recognition system from Apple) to control the music playback. Just do a long press on the home button (or microphone button on headset ) and say "Stop music."
The iPhone can automatically close the iPod app after a certain period of time. Go to the "Clock" app > "Timer"