Are Pilates and yoga the same thing?

No.  I’m no yogi so I don’t want to claim yoga is this or that. The little I do understand about yoga is that it is an old form of exercise both physically, mentally and spiritually that has many styles and deserving of its own book, which there are many. The most notable difference between yoga and Pilates from my understanding is that Pilates has an entire set of equipment that allows for resistance training in addition to the more familiar mat exercises.  Pilates also has no spiritual component to it.  It can become very meditative and relaxing for many due to its repetitive nature and the “mind body” aspect of Pilates. 

Is Pilates like yoga?

Pilates is not like Yoga, except that they are both forms of movement.  While Joseph Pilates did study Pilates and many other forms of fitness and mind-body disciplines, Pilates is a form of fitness and movement in its own right.  Pilates and yoga are complimentary exercises yet very different.  Yoga traditionally includes meditation while Pilates does not.  The breathing techniques of both practices are also quite different.  The breathing technique used in Pilates is more athletic or three dimensional in nature in that you inhale through your nose expanding the ribcage not only anteriorly but also posteriorly and laterally while maintaining engagement of the abdominals and core muscles minimizing the expansion of the abdomen while inhaling and then exhaling through pursed lips.  The breathing in yoga is to inhale and exhale through the nose.  Pilates is not just exercises on a mat.  There is equipment also available on which there is an entire repertoire of Pilates exercises.  These pieces of equipment provide resistance.  Pilates provides resistance training as well.