I've got ideas for posts which have been building up since I started studying. But now I'm too tired and elated to post them. Later this weekend, though. For now, I random stupid legal fact for non-New Yorkers:
There's a Federal judicial system. They've got branch offices in every state. These lowest-level courts are called District Courts. They're the trial courts of the Federal System; they hear pleadings, meet with parties, decide motions, supervise the actual trial, render verdicts as necessary, etc. They're the hands-on judges.
If you don't like a decision that comes out of a District Court judge, you can appeal it to the Circuit Court. There are 11 Circuits, plus the DC Circuit (which is one of the more important circuits, even though it covers the least area by far. It shouldn't be too hard to figure out why; it happens to be the court that covers federal law for the seat of the Federal Government, so a lot of administrative actions and government business goes through the DC Circuit). The circuit courts are intermediate appellate courts. They only hear very explicit challenges to the way a trial was run, or some point of substantive law, or whatever. Appellate courts don't hear trials; if they decide a new trial is needed they remand the case back to the district court with orders to try the case again and instructions on how to run it right this time. This makes some sense. Making decisions upon fine points of law is a fundamentally different activity than the labor-intensive work of managing trials and such. Why not divide the labor like that?
If you don't like an appellate decision, you can appeal to the Supreme Court. The Supreme Court is very busy. They don't have time to hear all the cases that are appealed to them, whereas the Circuit Courts do have to hear all appeals. The Supreme Court generally carefully picks its cases so that it only hears cases that will have a big impact, or that will resolve a niggling question. One of the interesting aspects of our system is that Circuit Court rulings are only binding in the territory of their circuit. So if the 9th Circuit decides that the US Constitution bans the Pledge of Allegiance, that interpretation is valid within the confines of the 9th Circuit, but nowhere else. It doesn't need the Supreme Court's certification to be binding; its rulings are the law of the land within its geographic jurisdiction, but only within its geographic jurisdiction. One of the surest ways to get the Supreme Court to hear a case, though, is with a circuit split. If the 5th Circuit rules one way on an issue and the 9th Circuit rules the complete opposite way, it's a good bet that the Supreme Court will take an appeal on that issue to resolve the dispute. Once a matter gets decided by the Supreme Court, it's binding on the whole country.
This is all prefatory. The US Constitution sets up the Federal system (vaguely; it defines the contours, but the meat is actually provided by acts of Congress). The states are free to set up whatever the hell judicial system they like (or no judicial system, in theory), subject to the constraint that they have to abide by the 14th Amendment's requirement that they give their citizens due process of law. Each state has its own unique variations, but most have adopted a system vaguely analagous to the Federal system, with lots of low-level trial courts, a few intermediate appellate courts, and one Supreme Court that is the final word on matters of state law.
We're closing in on the point. States can call these courts whatever they want, but as a general rule the nomenclature is something like "District Court" or "Trial Court" or, in California, "Superior Court" for the lowest level courts. The intermediate courts tend to be called "Courts of Appeals" or "Appellate Courts." In almost every case the highest court is the Supreme Court.
The one goofy exception, which you may have caught on to from Law and Order, is New York. For reasons that are beyond explanation, New York calls their trial courts "New York State Supreme Courts." Their intermediate courts are called "New York State Supreme Courts, Appellate Division," and the highest court for the state is the New York Court of Appeals.
That's all I've got.
One of my profs suggested that the name in NY was changed to Supreme Court because at some time the judges wanted a raise, but instead they got "promoted." However, I have never fact checked that.
Eh, sounds plausible. My guess is that it's for the same reason that the general trial courts in California are called Superior Courts; it's to indicate that they're the courts of general jurisdiction, superior in that sense to Small Claims Court, Family Court, Housing Court, etc. Still, it seems rather silly and stupid to use the name "Supreme Court," when every other state and the Federal Government uses that to mean "Court of Last Appeal." Also, the entire superior/supreme nomenclature to mean "general jurisdiction" is pretty dumb. Just because you're the catch-all court doesn't really imply that you're better than the specialty courts.