J.J.
You know, I've done both and I have a hard time describing the difference between the two. I'd say that both involve core muscles, but pilates seems to be more focused on those muscles. The yoga classes I've taken seem to involve more flow between movements and tend to focus more on centering and relaxation.
Regardless of the difference, I wanted to recommend the 10 Minute Solutions workouts. I bought several of these dvds from Amazon when my daughter was born, and they're great. They have quite a variety of workouts from kickboxing to fitness ball to pilates. These are great for sneaking in 10 minutes whenever you have the time, and it's nice when you do have 20-30 minutes to mix it up a little and do a variety of 10 min workouts. I do really like the pilates video, so this is one that I'd highly recommend if you're looking for short pilates workouts.