Federal judge
Federal judges are judges appointed by a federal level of government as opposed to the state / provincial / local level.
Brazil
In Brazil, federal judges of first instance are chosen exclusively by public contest. Judges of Federal Courts of Appeal or Higher Courts are appointed according to specific rules. Appeal judges of second instance are called Desembargador(es).
Canada
Canada is a federation composed of a federal (central) government and of ten provinces and three territories. There are two levels of courts in each province or territory (except Nunavut): superior (upper level) courts appointed by the federal government, and a provincial or territorial court appointed by the province or territory.
Judicial appointments to the superior courts (trial or appellate) in each province or territory are made by the Governor General on the recommendation of the federal cabinet. Appointments to other superior courts which have jurisdiction for all Canada ---the Federal Court, the Federal Court of Appeal, the Tax Court of Canada, and to the Supreme Court of Canada which is the final court of appeal from all Canadian courts---are also made by the Governor General on the recommendation of the federal cabinet. Appointments to the provincial court in each province are made by the Lieutenant Governor of the province on the recommendation of the provincial government.
United States
A United States federal judge is a judge appointed by the President of the United States and confirmed by the United States Senate in accordance with Article III of the United States Constitution. Judges for Circuit Courts, called "circuit judges," are also appointed by the President and are therefore also "Federal judges." Federal judges are appointed for terms of life.