Yeah, James pretty much said it...except Im a turbo nut for one reason. Here´s two ways you can increase boost in a turbo motor:
1. turn knob on the boost controller (takes a couple seconds)
2. Flip switch or press a button on more expensive boost controllers.
For a supercharger changing a pulley can take some work, and then you also have think, somtimes you may need a new belt for it too.
Other then that, both are forced induction methods. Both increase intake air charge temps, both require money and tuning. One thing Superchargers are great for are producing boost instantly. I spool pretty quick (5psi at 2800rpms) but a supercharger is instant.