In Buddhism like every other religious worldview comprises various concepts that are related and need to be understood within their interlocking relationship so that the picture as a whole is understood. When you talk of karma it is best understood in relation to rebirth because karma in its own is meaningless to some degree unless you relate it to rebirth and eventually nirvana which is the ultimate goal of all Buddhist. When you talked of karma as simply release from desires to enter nirvana, you are side stepping the fact that many cycles are required to get to the end state (if at all). Buddhist often describes the cause and effect relationship which basically is about the karma as a result of actions and the consequent continuous streams that crosses death and into the next existence. It is more than just relinquishing desires but the karma as a consequence.
The problem in our discussions I am concern with whether we are talking about the same thing because there are disagreements even among Buddhist between the different schools. In addition, the fusion of Hinduism concepts on Buddhism and that the same word might be used but the meaning is different depending on which perspective you are leaning from. For example, the terms moksha and nirvana are used as synonyms to describe release or freedom from the cycles of birth and death (samsara). Moksha is a process and not a state of being.
Finally, I am mindful that the subject is still about Chinese culture and Buddhism and not a discussion about deep Buddhist teachings that others have no interest in.