Does a Magic Trackpad have a button?
Yes, it has two physical buttons on the edge lacking the battery tray. The two rubber feet on the bottom-front of the trackpad press against  internal switches.

For these to activate, you have to use it on a hard surface. The software tap-to-click that senses your finger pad deforming as it taps the immovable glass surface also will trigger a tap independently from the physical buttons.