How is Pilates different from Yoga?

Both Pilates and Yoga are mind-body systems that focus on breath control.  Pilates is practiced on a thicker mat or on equipment where Yoga is done soley on a thinner mat.
Pilates works your muscles from the inside out.
Yoga focuses more on meditation, depending on the level and is usually practiced as a class with 5-20 participants(but can be one on one).  Pilates can be practiced in a class setting but is usually practiced privately one on one.