Federal monarchy, a federation of monarchies; Federation, or Federal state (federal system), a type of government characterized by both a central (federal) government and states or regional governments that are partially self-governing; a union of states; Federal republic, a federation which is a republic; Federalism, a political philosophy
A federal republic is a federation of states with a republican form of government. At its core, the literal meaning of the word republic when used to reference a form of government means: "a country that is governed by elected representatives and by an elected leader (such as a president) rather than by a king or queen".