Pausing it in essence is Stopping the music.
If you want to stop stop it pressing the button with the circle bottom of iPod touch will stop the music but also take you to the Apps page.
I have the same problem: I cannot switch off the music of my iPod Touch G2. When I pause the music it shows "Now playing" on the 'Shuffle' page. Even after I follow your advice and press the circle button, when I go back it still shows "Now playing". And it is still using up the battery when it is switched off.
As stated above, pause functions as stop. The program does not continue to use battery when paused.
You can "kill" the program outright by double-clicking on the home button to bring up the tray of recent programs, find Music, hold until the "x" appears and press the x. However, as already stated, this is unnecessary.
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