The State can have different structures; it depends on whether its functions are divided or not, and on how the Head of State is appointed.
According to the Division of Powers
The division of powers is the way the State’s functions are divided and organised. In a democracy each main function is assigned to a different public institution. The division of powers, one of the main features of modern states, means that the power is divided into three parts: the legislative power, the Executive power (or government) and the Judicial power. However, in a dictatorship or in absolute monarchies, there is no division of powers and all the power is in the hands of a single person or group.
Appointment of the Head of State
If the Head of State is an elected president, it is a position for a specific country and period. This is the practice in democratic republics, but there are also republics that are dictatorships.
If a king or a queen is the Head of State, it would be a monarchy. Leadership is in the hands of one person, who is not elected by the citizens, and his/her rule is for life, in other words, it is hereditary. The monarchy is linked to a historical tradition and its power in democracies is limited by the constitution. We call these regimes constitutional monarchies or parliamentary monarchies.
Territorial organisation
States can be organised in many different ways. There are larger states or unions consisting of states that are federated with each other, such as the Federal Republic of Germany of the United States of America. There are also centralised states where the power is completely centralised. Some states are divided into different autonomous territories or communities, and each territory has its own political powers.