Federal appellate courts are Circuit Courts of Appeal. Circuit Court in Florida is the state Court with general jurisdiction over $15k for Covil and felonies for criminal courts). It is the equivalent to CA Superior Courts. The same level courts in the federal system are district courts as they are in state courts on Colorado. The moral of this story is that each sovereign can call its courts whatever it wants to call them. A defendant cannot enter a plea in any appellate courts. The Florida Circuit Court must have been the court at issue in your politician's case.
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State trial courts come with various names. For example in the State of Florida, their trial courts are called "circuit courts." In New York, the highest level trial courts are called the 'supreme court." So yes in Florida you can plea in the circuit court, but it is the state court.
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Illinois, for example, has no Magistrates Court, no Superior Court, no District Court, no Surrogate's Court, no Orphan's Court (my favorite) no Appellate Division and no Court of Criminal Appeals, all of which are found in some other states. The Illinois trial court is called the Circuit Court. The court that hears appeals from the circuit court is called the Appellate Court. The state's highest court is called the Supreme Court. Every state sets up its own court structure and uses its own names.