A core desired mental state is what “really” motivates one’s action. It is the motivation that is revealed after repeatedly asking “Why?” after an individual has declared his purpose in acting a certain way.
On the other hand, one’s purpose is what one “believes” to be his motivation. If one is aware of one’s core desired mental states, one could see past shallower purposes for action and declare a certain core desired mental state as one’s purpose. For example, instead of saying, “My purpose in life is to be rich,” one begins to say, “My purpose in life is to be happy,” seeing that wealth is simply a vehicle towards a deeper core desired mental state.