To what extent do the decisions of appellate courts in the US (both
Federal and State), and particularly decisions of the US Supreme
Court, bind those who were not parties to the case?
A published opinion of a court regarding questions of law is binding precedent with respect to all issues necessarily decided by the court to resolve the issues presented to it in a case arising in a court whose decisions can be appealed to it (in a court whose decisions can be appealed to a court that can be appealed to it).
Thus, U.S. Circuit Court of Appeals decisions are binding precedents for the U.S. District Courts in its circuit (and on the bankruptcy courts and bankruptcy appellate panels in its circuit). Bankruptcy appeal panel decisions are binding on U.S. District Courts and U.S. Bankruptcy Courts in the appellate circuit, but are inferior to U.S. Circuit Court of Appeals decisions.
State supreme court decisions are binding on all state courts. Intermediate state court of appeals decisions are binding on the state trial courts whose decisions may ultimately be appealed to intermediate state courts of appeal (all of them if there is one intermediate state court of appeal, but only some of them if there are multiple intermediate appellate court districts in that state) and all courts to which appeals are taken to state courts if appeals from those state courts in non-appellate cases may be appealed to intermediate state courts of appeal.
A U.S. District Court, in one of the rare cases in which there is a direct appeal of right to the U.S. Supreme Court (e.g. election law cases) is still bound by the binding precedents of its circuit on any issue decided in the case upon which the circuit has binding precedents.
Similarly, for example, in Colorado courts of limited jurisdiction called county courts have their decisions appealed to courts of general jurisdiction called district courts, but further appellate review of a county court decision is made to the Colorado Supreme Court rather than to the Colorado Court of Appeals, an intermediate appellate court. But, despite that, Colorado Court of Appeals precedents are still binding in county courts in Colorado, because the District Courts to which it appeals are themselves required to treat Colorado Court of Appeals decisions as binding precedents.
But, federal court decisions on matters of state law (usually in diversity jurisdiction cases) are only persuasive precedents on these state law matters. Thus, if the (federal) U.S. District Court for the District of Colorado in a diversity case has to rule on a question of state law, a Colorado Supreme Court decision is more authoritative than a U.S. Court of Appeals for the 10th Circuit decision on the same subject, even though either would be a binding precedent on the U.S. District Court for the District of Colorado.
Conversely, a decision of a state's intermediate court of appeals is not binding upon federal courts on matters of state law, although they are highly persuasive. See, e.g., Clark v. State Farm Mut. Ins. Co., 319 F.3d 1234, 1240-1241 (10th Cir. 2003). A federal court may ignore an otherwise binding precedent of an intermediate state appellate court if the federal court concludes that the decision of that court was decided contrary to the likely holding of the state's highest court. See, e.g., DigitalGlobe, Inc. v. Paladino, 269 F. Supp. 3d 1112, 1122 (D. Colo. 2017). If a federal court is unsure how an issue of state law would be resolved in a state court, such as in a state law case of first impression upon which the state has no binding precedents, it can certify that legal issue to the state's highest court for a definitive resolution of the state law issue presented.
U.S. Supreme Court decisions are binding on all courts in the United States as to matters of federal law including interpretations of the U.S. Constitution.
Decisions of a court that does not have appellate authority over the court making the decision, unpublished decisions of a court, decisions of a court on issues not necessary for it to decide in the case before it which are called dicta, and authorities other than case decisions, statutes, and regulations, are merely persuasive authority. Some courts don't allow citations to unpublished decisions at all.
There are a few federal forums where this is particularly tricky. The National Labor Relations Board, the U.S. Tax Court, and the Board of Immigration Appeals (none of which are Article III federal courts), each serve as unified trial courts with a national territorial scope in their subject matter areas. But appeals from their decisions are to whichever of the twelve U.S. Court of Appeals for the Circuit in which the case arises (D.C. and Circuits 1-11). In those forums, the question of which circuit's decisions are binding and which are merely persuasive authority for the NLRB, Tax Court or BIA depends upon where the particular case before it arose.
And to what extent are Federal Court decisions binding on state
officials and courts?
Precedents and Federalism
U.S. Supreme Court decisions on questions of federal law including federal constitutional law and treaties, are binding on all courts. Federal court decisions on matters of state law are not binding on anyone but the parties to the lawsuit.
Federal court decisions on question of state law are not binding precedents on state courts.
The corollary of these rules, which is subtle, is that a decision of a U.S. District Court in a state, or of a U.S. Court of Appeals in a Circuit that includes a state, on a question of federal law, is not a binding precedent on state courts in that state or circuit on that question of federal law.
For example, suppose that the Colorado Supreme Court determines, without resorting to a separate state constitutional right, that the 4th and 14th Amendments to the U.S. Constitution's exclusionary rule for unlawful searches and seizures require physical evidence obtained in reliance on a lie from a law enforcement officers to be excluded from evidence at trial as an unlawful search, but the 10th Circuit in which Colorado is located reaches the opposite conclusion, and the U.S. Supreme Court has not ever made a ruling definitively resolving that issue. In that situation, the meaning of the 4th Amendment in state court criminal trials would be different from the meaning of the 4th Amendment in federal court criminal trials in the same state, even though this is a question of federal law.
This isn't to say that a binding 10th Circuit precedent on a question of federal law wouldn't be extremely persuasive authority to a state court on that issue of federal law in the State of Colorado (which is located in the 10th Circuit). But it still wouldn't be a truly binding precedent.
The Effect of Court Rulings On Parties To Federal Cases And Federalism
Federal court decisions on questions of federal or state law are binding on the state officials affiliated with the governmental official or entity that is a party to the federal court case.
For example, a decision of the federal U.S. District Court for the District of Colorado in a case to which a Denver policeman is a party (with respect to something done by him in his official capacity as opposed to his private life), is binding upon all officials in the City and County of Denver, and on the City and County of Denver as an entity, even if only the policeman is a party to the lawsuit in federal court. But that ruling wouldn't be binding on the State of Colorado or the City of Aurora, which are different governmental entities.
Determining whether a particular government official from an agency, or a particular agency, is part of a state government, or of a particular local government, or is an independent governmental entity in its own right (e.g. in the case of the C.U. Regents of the University of Colorado), is not always a self-evident question and often would require fact specific legal analysis to determine.
If someone is ordered to do irreconcilable things by both a federal court in an order binding that person, and a state court in an order binding that person, the federal court order prevails over the state court order.