Through the practice of both yoga and Pilates you will experience many benefits. While there are some similarities between the two, the background and focus of each is somewhat different.
Both will improve your balance, flexibility and strength, as well as increasing your mind-body awareness and control. Both have a strong focus on breathing and are great for stress-relief.
In terms of their origins, one is a holistic discipline originating from ancient India, the other a specific physical system devised by a German anatomist called Joseph Pilates in the early 20th century.
Yoga incorporates more spirituality and meditation and can incorporate elements of philosopy, science and an ethical way of living. Pilates originated with 34 exercises, largely focused on core strengthening and can incorporate various small and large equipment and machines which allow numerous modifications for different conditions and rehabilitation requirements.