Dharma and Karma are extremely complex ideas but some aspects of them are:
Dharma is a rule or pathway. Many actual rules are set by the Manusmrti.*
Karma is action. "Good" karma is achieved by following one's dharma.
Properly following one's dharma leads to advancement in one's next life.
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*The Manusmrti, also known as The Laws of Manu is a Sanskrit legal text. Its origins date to the era between 200 BCE and 300 CE. There are numerous versions and much controversy surrounds it. However, it is the key source for identification and behavioral regulation of the varnas, the rules of karma, rebirth, and liberation, as well as numerous other areas of theological understanding and social behavior.