A federal republic is a federation of states, with a republican form of central government. It differs from a unitary state in that in a federal republic, the authorities of the state governments cannot be taken back by the central government.
Many countries have a federal republic government; for example, the Federal Republic of Brazil, the Federal Democratic Republic of Ethiopia, the Federal Republic of Germany, the Republic of India, the United Mexican States, the Federal Republic of Nigeria, the Islamic Republic of Pakistan, and the United States of America. As this list shows, some of these countries use "Federal Republic" in their name, and some do not. Federal Republics usually have presidents.
There can be more than one type of Federal republic. For example, the United States is a Constitutional Democratic Federal Republic.