Yoga is a spiritually based movement practice that uses breathing, meditation, chanting, stretching and careful control of the body by focusing the mind to achieve enlightenment. There are many different types of yoga, the most popular types of yoga in the united states use the technique of moving slowly into a pose and holding the pose while taking slow deep breathes in order to achieve a quieting of the mind.
Pilates is a secular movement practice (meaning it has no religous affilliation) and uses breathing, stretching and careful control of the body by focusing the mind. Pilates focuses on abdominal strengthening and functional use of the muscles and joints. There is a large focus on anatomy and learning how to feel and differentiate different muscles in order to achieve healthy and strong hip joints, shoulders and spine. Pilates uses the ideas of stability and mobility to teach practitioners how to keep themselves from being injured even when they are doing very complex actions (like ballet or kite surfing) and the focus is fitness.