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.