Judge: For practical purposes, this really means only one thing: the person in charge of the court who is called "judge." In the legal sense, though, there can be significant differences. If you're in federal court, you could have a full judge or a magistrate, and sometimes a "special master." Normally the magistrate judge will have full power, but since magistrates weren't put in place by constitutional rule, you might have to elect or approve the jurisdiction of the magistrate. That could give you some opportunity to "forum select" (choose who is your judge by researching a little about the magistrate). In state court you could have circuit judges or associate circuit (or magistrate) judges. Sometimes you have choices based on state court laws as to whether you have to accept one of these.
A "special master" is somewhat different. That's a person--not always even a real judge at all--appointed by the judge to hear preliminary disputes and issue preliminary rulings which can be appealed to the judge.
An "arbitrator" is yet another thing. In some courts, they automatically refer and require arbitration. In at least some of these (all that I know of), the arbitrator's ruling can be appealed "de novo," meaning that if you didn't like what the arbitrator did, you could start all over again in court with a judge. If there is an arbitration agreement, however, this is normally not an option, and the arbitrator is going to issue a ruling which is binding, with certain limited rights of appeal.
Judgment: The court’s final ruling as to all the issues in the case between two litigants. It terminates the suit, it isn’t just a step along the way (compare to “Order”). After the jury reaches its verdict, the court will consider certain issues and then make its “judgment,” which will incorporate or disagree with the jury’s verdict, and it is the judgment you will seek to enforce or from which you will appeal, although you can also appeal orders.
Jurisdiction: there are two important definitions of this term. First, it refers to what court and whose law applies to a specific case. If you live in the City, some cases against you could be brought in municipal court (typically not debt cases, though), some in the state circuit court for whatever county you live in, and some in the federal district court for your district. In other words, jurisdictions can overlap. If the suit against you is filed in the Circuit Court of the County, the County Circuit’s Local Rules will apply in addition to the State Rules of Civil Procedure and Evidence. If you file suit in the Federal District Court, then the Federal Rules of Civil Procedure and Evidence will apply as well as the Federal District’s Local Rules.
Jurisdiction also refers to the power of the court to hear the lawsuit against you, and this requires both that you have been served with process (or that you waive it—let it go)(giving rise to what is known as “personal jurisdiction”) and that the court has power to hear that kind of case (this is known as “subject matter jurisdiction,” which cannot be waived). Federal courts typically do not have subject matter jurisdiction over traffic law cases, for example, even if the parties agree that it should.
Jury: A group of people drawn, more or less at random, from the community. After a process known as "voir dire," the jury is selected and "impannelled," and they are the ultimate fact finder in the case and will resolve all significantly contested issues of fact (whether or not something happened). The judge decides what the law is and tells the jury how to apply that law to the facts they have found through jury instructions.
Jury instructions: Specific instructions which the judge gives to the jury explaining how to apply the law to facts that the jury believes are true. In some states, these instructions are kept in a book called “Approved Instructions,” but in other jurisdictions there may or not be an official collection of “approved” instructions. You can find instructions used by other people by looking up the files of cases that actually went to jury trial, or you can ask for some research guidance from the law librarian at a university law library. Jury instructions are considered so important that they are frequently appealed and often discussed in great detail by the courts of appeals
Jury trial: A trial conducted before a jury—a group of citizens selected by the plaintiff and defendant from a random drawing. The jury is primarily responsible for finding the facts of the case and applying the facts in ways guided by the jury instructions. The opposite of a jury trial is a “court-tried” case, or a “judge-tried” case, in which there is no jury, and the judge is the person who finds the facts and applies the laws to them.