A republic is defined as a form of government that is ruled by the people and their elected officials. The country is considered to be a “public matter” and is not the property of the person that rules the country. Positions of power are not inherited, such as with a monarchy, but instead are obtained through autocracy, oligarchy, or democracy.
There are many nations that use the word “Republic” in their official names. However, not all of these nations have a republic form of government. In the same sense, not all nations that actually have a republic form of government have the word “Republic” in their names.