Federal judges are judges appointed by a federal level of government as opposed to the state/provincial/local level.
A US federal judge is appointed by the US President and confirmed by the US Senate in accordance with Article 3 of the Constitution. The US Supreme Court currently has 9 justices. The judges of 13 circuit courts of appeals and 94 federal circuit courts are also appointed by the president and are therefore also "federal judges" (or Article III judges). Federal judges in the United States are appointed for life (impeachment through the US Congress is possible).
For 2018, Article III judges include 807 judges: 9 in the Supreme Court, 179 in the district courts of appeal, 673 in the federal district courts, and 9 judges in the federal court of international trade. 
The judicial system of the Russian Federation does not define the concept of “federal judge”, but provides for the position of a judge of a federal court. At the same time, all judges in the Russian Federation have a single status (Article 2, Part 1 of the Law “On the Status of Judges in the Russian Federation”). As of 2009, there were 23,297 federal judges in the country in the general court system. Judges of federal courts are appointed by the President of the Russian Federation, and judges of the Constitutional and Supreme Courts are appointed by the Federation Council.
In the words of the Federal Constitution, the judge is an organ of the Judiciary. Thus, he is an agent of the State, responsible for saying the Law definitively. Specifically in the case of the Federal Court, the judge is responsible for judging the actions in which the Union, its autarchies and federal public companies are, in some way, interested. In addition, it also judges other matters, such as those involving foreign States, the dispute over indigenous rights, cases relating to nationality and naturalization, and the execution of foreign judgment.
In criminal matters, among others, it judges political crimes and criminal offenses committed to the detriment of goods, services or interests of the Union or its municipal entities or public companies, crimes against the organization of work and, as a general rule, crimes committed on board ships or aircraft.
- United States Courts. "Chronological History of Authorized Judgeships - Courts of Appeals".
- Marcus, Ruth (June 7, 2021). "Opinion: The truly worrying aspect of a federal judge's ruling on assault weapons". The Washington Post. Archived from the original on June 9, 2021. Retrieved June 9, 2021.
- Veiga, Paula (2014). O que faz de um Presidente da Republica um Presidente Republicano? : Paradigmas. doi:10.14195/978-989-26-0758-0. ISBN 9789892607580.