Under the Judiciary Act of 1801, the United States federal judicial districts were divided into six (and later seven) United States circuit courts—one for each justice.
Rather than appointing separate circuit judges (with the exception of the brief interlude under the soon-repealed Midnight Judges Act), the circuit courts were staffed by a combination of the resident United States district court judges from that district and the Supreme Court justice assigned to that circuit (either could preside alone or they could preside together).
While the circuits were the unit of circuit riding assignments, the individual circuit courts were referred to by the name of the judicial district (e.g. "United States Circuit Court for the District of New Hampshire," or, in case citations, C.C.D.N.H.).
Some districts were not within any circuit (for example, under the Judiciary Act of 1801: Maine, Kentucky, and Tennessee).
Circuit riding did not occur within such districts.