Both Pilates and Yoga are holistic disciplines that focus on mind and body. The main difference between them is the spiritual approach. Yoga focuses on connecting mind, body and spirit, while Pilates focuses on proper alignment of the body, core strength and performing the exercises in a precise and controlled way, using diaphragmatic breathing.
Another important difference is that Pilates involves more movement. You can use different equipment if you perform Pilates on the mat, like the ring, hand weights, ball, band, mini band, Swiss ball. Or you can make use of specialised apparatus, like the reformer, the chair, the tower and the Cadillac.
Yoga is mat based, with only a few extra pieces of equipment. It requires less movement, and more focus is given to holding poses that challenge your core, concentration and flexibility.
Both are great forms of exercise that do not stress the body. You can try both and see what you enjoy.