How is Pilates different from Yoga, anyway?

I was doing an "Ask the Expert" session last week in a facebook group, and this question came up predictably quickly: What is the difference between Yoga and Pilates? I definitely hear this one a lot from family, friends and prospective clients. Most people out there know a bit about yoga and not much about Pilates. I have only been to a handful of yoga classes so I often shy away from speaking too much about yoga. I could talk your ear off about Pilates for hours but my yoga knowledge is very limited! But I gave it some serious thought last week and I came up with the response below. If you are a yoga teacher and have a differing opinion on the topic, please do join in the conversation in the comments below, I'd love to hear more from you about it!

"I can start with what they have in common: both exercise systems use the mind-body connection. That means there is an emphasis on using your mind to move your body, concentrating and focusing on your movements. And both systems use your own bodyweight as a resistance for building strength. But after that they differ a lot! Pilates has a focus on building muscle strength and stability in the core (your torso- including your hips and shoulders). There is more dynamic movement in Pilates and an emphasis on lengthening while strengthening. Yoga is more stationary (holding poses) and emphasizes flexibility. Yoga can include a spiritual aspect, while Pilates does not. Pilates is highly adaptable and therefore great for injuries and back problems. I can't speak to yoga that much because I don't know that much about it... and there are lots of different types, however in my experience yoga has a flow to it where there is a prescribed series of positions moving from one to the next. But for me, when I'm planning a class, I think carefully about who is coming and what injuries they might have and what modifications they might need, and I prepare a set of exercises with modifications specifically for them. I get to be incredibly creative and that's one of my favourite things about teaching pilates- as long as I keep to the 6 pilates principles, I can modify any movement for anyone. :-)"

If you've attended both types of classes, does this explanation ring true for you? Please share your thoughts below! Thanks :-)