This is the question that Pilates instructors are often been asked and usually come with "Is it like Yoga?".
Not quite but if "Doing exercise on a mat." is the definition of Yoga, in that case yes it's like Yoga but Pilates also has exercises with specialized machines too.
In my opinion "Pilates is about understanding own physical body and practice effective way to use it, so you don't get hurt and get better result and benefit from your daily activity".
We think we know how to use our body but usually that is not the case because human body is really adaptable, so we can use it in many different way.
Unfortunately this doesn't mean we won't have problem. It is adaptable but we will have issue at some point unless we use our body in the way our body should be used.
That's why it's important to know and practice kind of movements that good for your body.
One big difference between Pilates and Yoga is the Breathing.
Pilates focus on "Lateral breathing" this is opposite of "Abdominal breathing"in Yoga.
In my opinion we have to practice "Lateral breathing".
Most people has tight chest and shoulders which makes really hard to fully expand the chest causes shallow breathing and if the chest and shoulders remain tight it will restrict the healthy movement of the spine.
That's why lateral breathing is so important in Pilates.
It is not easy thing to practice but if you can improve lateral breathing it will help you relax your chest and shoulders, as the result it will make easier to practice healthy spine movement.
This breathing and spine movement is some of the important things in Pilates but also good example of how we approach human body in Pilates exercises.