I would like someone I could explain in a simple way the difference between republic and democracy. The truth that I don't know if they are words antagonistic, or can they go hand in hand. The definition of each a the I understand it, what I do not understand is that they distinguish the two words as for example in France there is democracy and at the same time it is a republic. Well I made a mess!.
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It's not about expressions antagonistic but of different things. 1\.- The Republic is a form of government. We would be talking about the way to organize the headquarters of the State. Normally is opposed to the monarchy. In the first it would be a political office and eligible and in the second it would be a hereditary post. It is not better than the other, are different. In both cases there are different modes of organization. Republics tend to be presidencialistas or parliamentary. In the first it is the people who elects the president or head of state, and in the second it is the parliament that elects him. In some and in others the powers of the president are different. Examples of the former we have in the usa. US or in some republics of South america, and of the latter are found in Europe in countries like Germany or Italy. The case of France is a bit particular because it is a Republic with presidential system with respect to the system of election of the president but, formally, it is a parliamentary Republic because the Government needs the confidence of Parliament. 2\.- Democracy is a mode of election of the rulers of a given State. We have two modes of exercise of democracy: direct or by representation. The democratic exercise direct is a mode of government in which the decisions to be taken by the government are subject to a consultation at the subject to exercise democratically the sovereignty of the people. Example of this mode is found in the Helvetic Confederation (Switzerland). The exercise of democratic representation is a mode of government in which what you choose to the sovereign subject are the representatives. Will be these who, in the exercise of the representation they hold, the decisions of government in parliament. Examples of this are the thousands, starting with Spain. To be able to delve more into the concepts and their meaning can be begin by the reading of classical authors such as Plato or Aristotle, following by Niestzsche or Hobbes, to terminate any Treaty or study on constitutional law that are studied in Universities.
We are not experts in this matter, and for sure someone can help you more academic. But in our opinion: A republic can not be a democracy. That is to say, usually a distinction is made between republic and monarchy (there may be some more), which is not more than the determination of the Head of State by election or by inheritance. Democracy is a formula for election, by the vote of the citizens (usually). Spain is a democracy but it is a Kingdom, not a republic. Although as with everything in life, there are times that not just a simple name... as there are republics that are inherited, or at least it elects the president of that republic by a democratic approach among all citizens. In some countries, the single party choose the president of the republic "popular".
Republic refers to a system of government where there is a king (res publica: the thing published). Democracy a system of government in which power emanates from the people (demos: people, cratos: power). Are different dimensions of the political organization of a people or state, and these concepts are combined, for example France in a democratic republic( there is no king and the people elect their leaders), Spain is a monarchy democratic( there is a king and the people elect their leaders), for the opposite case, there is the example of Ancient Rome, in which in situations of exceptionality appointing a dictator to lead the Republic, with what they had, temporarily, a republic not democratic.
Democracy is the form of government where the people, the voters, elect their rulers. When in democracy there is a king who seems to have been inherited from fathers to sons of the reign, is called democracy contitucional, because the king is due to the Contitición. When in democracy there is no king, but elected a president of the government, is a republican democracy. Example, Spain, constitutional democracy. The king is Felipe VI. Example, the united States, republican democracy. The president is Obama, and every 8 years there is that change necessarily.