What is the difference between Yoga and Pilates?
As a practitioner of both genuine Yoga and genuine Pilates the difference to me is: Pilates is a more scientific approach to Yoga Asana (exercise) where control and anatomy pay a heavier role in a Pilates class. The difference is not really "How long you hold the pose", "how much you flow" etc. Those views are cosmetic and pre-dominantly Instructor and training specific and as a result end up being common myths.
Pilates is controlled Yoga similar exercises, whereas Yoga has a very heavy mindfulness component on top of the exercise (Asana).
Over the years I have heard and read many comments on both sides, some views rightly so, with regards to the relationship between the two disciplines. For e.g. "I do not like Yoga because..." , "I do not like Pilates because...", "Pilates is not influenced by Yoga...", "Pilates is better than Yoga ( or Vice Versa)....".
We need to step back and really consider our judgements. Genuine Yoga teaches us to not let our own ego to control the mind so, how come we allow ourselves to judge ?, isn't that ego? Maybe we were not experiencing genuine Yoga?
Pilates taught correctly does not hurt your back, so how come we do not like the whole Pilates Method discipline? Maybe we were not being taught appropriately or maybe our mind was not in our own movement?
Sometimes these judgements are all our own false perceptions based on certain bad experiences when participating. How can our own experience determine the fate of the whole discipline? Maybe it was that instructor? Maybe it was the number of people in attendance? Maybe it was our own mind and our own limited experience? Maybe it was the time of day and the year :).?

In my own experience both disciplines complement each other, rather than clash with each other. No one discipline is better than the other. Both disciplines work together as a team, both move the body, both help with flexibility, both disciplines help with movement of joints, both help with injuries, both help with pain management etc but maybe the approach is different, not wrong, but different.
In the spirit of Yoga, approach every experience with an open mind. Change is good, and varied regular experience is even better.
Yoga is a full system of mind and body, with emphasis on the mind and thoughts, movements find freedom of mind and body, whereas Pilates is also a mind body exercise system, but movements have order and Pilates uses controlled movements. Both disciplines use the breath to help our movement, and when you look at the breathing technique in Pilates, Pilates breathing is very similar to Yoga Ujjayi breath! Both disciplines overlap quite a bit, but they are different in their approaches and mindfulness.
Yoga unlike Pilates is letting go of that control of the mind and body to a certain extent and not allowing external happenings to affect mind and body. What I take from my Yoga classes into Pilates is letting go, and not controlling the movement to the degree that there is a loss of movement, as fear and control can cause lack of movement. What I take from Pilates into Yoga is to work from the centre of the body and not to let the body hyperextend to find that freedom within the body for e.g.
Hence, I will not teach genuine Yoga and genuine Pilates Method together as their approach and focus is not the same and in a way, do clash when taught together using the same controlled approach.
Both disciplines, in their genuine form, can co-exist and complement each other very well in our world of movement experience. It does not really matter which discipline came first, or which discipline influences the other. The body can only move in certain directions, eventually, each exercise system whether it be in a gym, whether it be in a physio or whether it be in a studio will move the body in a very similar way but what will be the difference is the approach, the depth of subject knowledge, the outcomes of your movement practise and, your own open mind approach.
At ShanthYogaPilates you will be taught close to original disciplines with Diploma qualified Instructors in the discipline itself (not a 3 day certificate for e.g.), and the outcome will always aim to change the mind and body, aim for change that is not an instant fix, but is a change that becomes second nature. The changes are both physical change and they are a change to the default mental response.
Both Yoga and Pilates at ShanthYogaPilates do influence each other heavily and complement each other.
I love them both, that is why I participate and teach both in their genuine form.