I'm no expert, so forgive me if this explanation isn't detailed enough but I've practised both.
Yoga is holistic. You hold poses and move through a series of poses and the correct breathing is vital. Some people do it for exercise, but I believe purists would say that your body looking good is just a side effect, as yoga is at its core a spiritual practise. As Melisande said above, "Yoga means "union"...union with your true self, with your own body, with God, with the universe, with nature, with friends and family...so just feeling that, being thankful in the feeling of oneness, helps your pracitce and life tremendously."
Pilates is not holistic, and does not involve any meditation or spirituality. It does not involve poses, it involves exercises which target your core muscles. By core, I mean the deep abdominal muscles (transvere abdominus sp?), not the superficial muscles which comprise a "six pack". It's all about the inner corset. It also works on your back muscles and pelvic floor. It doesn't look quite as graceful as yoga either, lots of lying on the floor with legs flailing about.....well, very controlled flailing!
I used to practise ashtanga yoga but it's way too expensive here in Dublin and there are hardly any classes. I live in the city centre and it can be almost €20 ($24) a class!! I thought about Bikram (€15 a class) but I get light-headed in a sauna
. I currently do Stott Pilates and my teacher is fantastic and my *God* is her body an inspiration. Kind of SJP...small but perfectly formed
I'd recommend if you're doing either that you get recommendations for an instructor - I couldn't make it to my usual Pilates classes so I enrolled in my gym and the teacher sucks. She's a physiotherapist and I swear the woman bought a video, did it a couple of times and calls herself an instructor. A chillout music CD does
not a teacher make!