Yoga is different to most forms of exercise in that it emphasizes the synchronizing of breath with movent, it includes balance exercises and inversions (poses where you are upside down) with a heavy emphasis on flexibility.
Pilates also emphasizes the synchronizing of breath with movement but is unique for its emphasis on the building of core strength together with correct alignment of the spine.
A typical yoga class will lead to greater flexibility than a Pilates class and will tend to improve balance more because of specific balance exercises and inversions. A typical Pilates class will tend to improve and maintain back health better than a yoga class because more of the class will focus on exercises to strengthen core and to maintain neutral alignment of the spine. A typical Pilates class will tend to focus more on your mid-section, toning up and strengthening the area around the abdomen, the tummy and the lower back. Yoga has a more global focuse and so does not focus so much on core and mid-section.
Pilates has more of a musculoskeletal focus while yoga pays as much attention to the effect of poses on internal organs and on your state of mind, with attention drawn inwards or towards the breath. A yoga class may include some meditation and relaxation while a Pilates class tends to be all physical exercise.
I hope this helps clear up the differences a little bit. I teach and practice both, finding them a perfect complement to each other. Of course to really understand the difference you need to come and try out a couple of classes, so check out our timetable if you would like to experience what the diffrence really is. Trial classes are always free.
Look out for some Youtube clips coming soon to demonstrate some obvious differences between the two.