A state that is ruled by an elected citizen is a republic.
A republican form of government is that which has a head of state elected by the people. This means that a sovereign state is referred to as a republic if the country has no traditional ruler of his representative as its head of state but by the one chosen by the people with a fixed term of office. Such head of state is known as a President in a republic. The President may be an Executive of Ceremonial President.
Some of the characteristics of a republican form of government is that the head of state known as the President is elected by the people.
In a republic, members of the legislature are directly elected by the people etc.