The U.S. District and Circuit Court of Appeals are federal
courts. Virginia Circuit and District courts are state
courts. The courts are not part of the same legal jurisdiction, and while they cooperate with each other in certain matters, there is no legal connection between a state district and federal district court, or a state circuit and state district court.
The hierarchy of state courts is that circuit courts are above district courts. The same hierarchy exists in federal courts
. However, because federal courts are superior to state courts, a federal district court can exercise authority over a state circuit court on matters of federal (but not state) law.
Yes, it's confusing as hell, and it gets worse, but there's no reason to consider further ramifications.
For purposes of your question, a federal district court judgment, which is apparently what you have, has a 20 year enforcement life. The judgment can be domesticated by the state circuit or district court, which could limit enforcement under state law. However, because the judgment would remain enforceable under federal law, if the state law enforcement authorities were to refuse to enforce after 10 years, the judgment creditor
could use the federal marshal to enforce the judgment for the remaining 10 years.
Please let me know if I can clarify or further assist.