Yes, there is a very important difference between mandatory authority and persuasive authority for courts and judges in the American legal system. If a decision is mandatory authority, it means that a lower court has to follow that decision. If a decision is persuasive authority, it means that a lower court can follow that higher court decision but does not have to do so.

The basic rule is that lower courts must follow the decisions of higher courts in their jurisdiction, while they do not have to follow higher courts not in their jurisdiction. Take the example of a federal district court in Tennessee, which is located in the purview of the 6^th U.S. Circuit Court of Appeals. This means that for the federal district court in Tennessee, Sixth Circuit decisions are mandatory authority, while decisions from the other circuits are persuasive authority.