Both can be used to as re-building tools however Pilates is more known for reducing physical pain and a great way to recover from an injury. Yoga is more used for emotional and mental rehabilitation, however it can build up physical strength as well as flexibility.
Yoga is an Indian practice over 5,000 years old. Over the years many different types of Yoga has evolved in different cultures. Some of these include; Ashtanga, Kripalu, Bikram and Vineyasa.
Pilates is much younger practice which was created by an athlete called Joseph Pilate. It dates back to the mid 20th century, the exercises were created as methods of strengthening and rehabilitation. Pilates became popular through dance as many began to use Pilate practices to strengthen their muscles for dance.
Both Pilates and Yoga acknowledge the connection between body and mind however Yoga brings in the spiritual side.