The terminology's confusing, but there's a court named the Court of Appeals for the Federal Circuit [1], even though the term "federal circuit court" also colloquially means the Courts of Appeals in general. This Federal Circuit is a non-geographical Court of Appeals, separate from the 11 numbered, geographically based Courts of Appeals, and has exclusive jurisdiction over patent cases (among a few other things). They also have a reputation of being very pro-IP-plaintiff compared to the courts in general.
Ah, so the "Federal Circuit" is another court at the same level as the other circuit courts that doesn't have a number associated with it. The choice of abbreviation is confusing to say the least.