It's less that there are two types than it is that they're complementary aspects of a larger thing. You can avail yourself of one — to great (if incomplete) benefit, even — without availing yourself of any of the others.

The way Yoga is practiced in the US and most of the world is just a set of exercises. Without the spiritual & mindfulness it is not Yoga as it is meant to be. Yoga is designed to be the complete package, not just for your body, but also for your mind, your thoughtfulness & soul (atma).