Democrac, Republic & Political Systems

Democracy is a form of government in which all eligible citizens have an equal say in the decisions that affect their lives. Democracy allows eligible citizens to participate equally—either directly or through elected representatives—in the proposal, development, and creation of laws. It encompasses social, economic and cultural conditions that enable the free and equal practice of political self-determination..
Democracy contrasts with forms of government where power is either held by one person, as in a monarchy, or where power is held by a small number of individuals, as in an oligarchy. Nevertheless, these oppositions, inherited from Greek philosophy,
A republic is a form of government in which affairs of state are a "public matter" (Latin: res publica), not the private concern of the rulers. In a republic, public offices are appointed or elected rather than inherited, and are not the private property of the people who hold them. In modern times, a common simplified definition of a republic is a government where the head of state is not a monarch. Currently, 135 of the world's 206 sovereign states use the word "republic" as part of their official names.
The term republic originated from the writers of the Renaissance as a descriptive term for states that were not monarchies. These writers, such as Machiavelli, also wrote important prescriptive works describing how such governments should function. These ideas of how a government and society should be structured is the basis for an ideology known as classical republicanism or civic humanism. This ideology is based on the Roman Republic and the city states of Ancient Greece and focuses on ideals such as civic virtue, rule of law, and mixed government.

A distinct set of definitions for the word republic evolved in the United States. In common parlance a republic is a state that does not practice direct democracy but rather has a government indirectly controlled by the people. This understanding of the term was originally developed by James Madison, and notably employed in Federalist Paper No. 10. This meaning was widely adopted early in the history of the United States, including in Noah Webster's dictionary of 1828. It was a novel meaning to the term; representative democracy was not an idea mentioned by Machiavelli and did not exist in the classical republics. Also, there is evidence that contemporaries of Madison considered the meaning of the word to reflect the definition found elsewhere, as is the case with a quotation of Benjamin Franklin taken from the notes of James McHenry. Where the question is put forth, "a Republic or a Monarchy?"
The term republic does not appear in the Declaration of Independence, but does appear in Article IV of the Constitution which "guarantee to every State in this Union a Republican form of Government." [WIKIPEDIA]