What is the difference between the mandate rule and the law of the case doctrine?

The mandate rule and the law of the case doctrine are frequently cited without differentiating one from the other. "There certainly is a difference between the two doctrines, and they are not identical. While both doctrines serve an interest in consistency, finality and efficiency, the mandate rule also serves an interest in preserving the hierarchical structure of the court system." United States v. Thrasher, 483 F.3d at 982. "The mandate doctrine is 'similar to, but broader than, the law of the case doctrine.'" Id.