Desirable means that it has qualities that you think would make a lot of people want it. There's generally a lot of agreement about what things are desirable. When you say something is desired, you are saying that it would make a particular person want it. Example: Being in good physical shape is desirable. Cindy wants to loose 5kgs to reach her desired weight. They are both natural and used, desirable is simply more general than desired.

Desirable refers to a property of an object or activity or person. Desired refers to such an object, activity, or person being the subject of one or more person's desire. Example: The car is desirable because of its excellent quality. The car is desired by many people.