Answer: dynasty = succession of generation in paternal lineage (or in some societies in maternal lineage). The word "dynasty" implies sucession and mutual family relations but does not imply social status of a such a family. Dynasty does not have to be royal to be a dynasty. Mandate of heaven = divine right of kings, i.e. supranatural (divine) will predestines someone to be a king, Dalai Lama, pope etc. "Heaven" is usually associated (not only in the West) with the spirit.
Explanation: whereas the first term has to do with bond of blood (family relation), the second term has to do with the divine intervention.
