Unlike the traditional exercise that is goal-oriented, Yoga is a process. The notion is to teach yourself how to be conscious of what you are doing and what you are feeling when you are doing the poses. In a standard exercise, you fail if you do not reach your target. In Yoga, every time you try, you are making progress.
On the physical level, normal exercise like weight training strengthens your body. Your muscle tissues are broken down and rebuilt. This process causes your muscles to have a bulky look. In Yoga, your strength is increased when your muscles are toned.