Our core desire is the force or energy within us moving our life. The defining characteristic of core desire is that its form independent — it works within and through whatever life circumstances (karma) we are in, moment to moment, irrespective of circumstance or manifestation.
Our assumed desires, on the other hand, are form dependent — they involve specific goals, ideations, or fantasies we fixate on and assume we must acquire, go through, or accomplish in a certain manner. It does not work within and through any life circumstances we are in, but rather within a narrower set of possibilities.
Though founded on some level of ignorance, assumed desires are still important in providing a rough roadmap for our core desires to explore. However, the illusion of assumed desire must ultimately be broken apart and seen through as well.