There is only one Supreme Court of the United States; however, each state has its own "supreme court," although a few name theirs differently. (For example, the highest appellate court in New York is the New York Court of Appeals; the supreme courts are their trial courts).
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There is only one Chief Justice of the United States at a time for the same reason all executive offices are filled by a single person: If more than one person occupies the top spot, there would be unresolvable political and personal power struggles that would disrupt the business of the Court.
The Framers of the Constitution realized the Judicial Branch needed a final authority on the law, and recognized that having more than one Supreme Court could create conflicting decisions that couldn't be resolved.
The US Supreme Court is the only court specifically mentioned in the Constitution; none of the other federal courts, past, present or future, was mentioned.
The US Supreme Court is the highest court in the US. Each state has its own Supreme Court, but the US Supreme Court is the end of the line.
The US Supreme Court (formally: The Supreme Court of the United States)
The correct name is the Supreme Court of the United States, but most people refer to it as the US Supreme Court. Each state has its own Supreme Court, but the US Supreme Court is the end of the line.
The hierarchy of federal courts is District Court, Court of Appeals, US Supreme Court. So, the Court of Appeals is the answer. At least if your quest is only specifying the federal judiciary.