Are Yoga and Pilates related? If so, how? Or are they completely different activities?

Yoga and Pilates are not really related.

They have different purposes and different effects on the body.

Here is a history of how Joseph Pilates developed his system. He had studied yoga among other things, but the movements are his own. It is particularly useful for strengthening your core muscles.

Yoga is far more ancient. It is a spiritual tradition designed to coordinate mind and body. It has many forms. In the U.S., many people practice yoga for its health benefits only. While traditional yoga is based on slow movement, there have been offshoots of “hot yoga” designed for the Western “do more, quickly” mindset. To me, that is diametrically opposed to yoga principles.

Yoga rewards practitioners with much greater flexibility and balance among other things.

Marina’s answer is very good.

I do want to point out that they are often referred as being similar, because they both allow the person practicing to improve their muscle tone and flexibility at their own pace in a controlled manner; while being more gentle and low-impact as compared to lifting weights or aerobic-type exercises.

They also do not increase the bulkiness of muscle as weightlifting does; nor do they burn calories/fat as effectively or have the cardiovascular benefits of aerobic exercises.