Federal Districts are subdivisions of a federal system of government. These districts are not generally considered to be one of the countries' component states and should not be confused with them, but are rather separate entities under the direct control of the federal government. The seat of the federal government is often located in a Federal District, so that no single individual component state can exercise inappropriate influence over federal affairs.
In the U.S. federal court system there are District Courts, which are sometimes referred to as Federal District Courts because the federal court system divides the country into federal judicial districts.
The U.S. Federal Reserve central banking system consist of 12 Federal Reserve Banks each of which is responsible for a Federal Reserve District.