The United States is a Republic not a Democracy.

Definition
Democracy - is ruled by the omnipotent majority. In a democracy, an individual, and any group of individuals composing any minority, have no protection against the unlimited power of the majority. It is a case of Majority-over-Man.

Republic - A republic is similar to a representative democracy except it has a written constitution of basic rights that protect the minority from being completely unrepresented or overridden by the majority.

Constraints on the government
Democracy - No; the majority can impose its will on the minority.

Republic - Yes; the majority cannot take away certain inalienable rights.

Philosophy
Democracy - All eligible citizens get equal say in decisions.

Republic - All eligible citizens get equal say in decisions with protection of unalienable rights to individuals.

Famous Examples
Democracy - Classical Greece, Rome
Republic - United States Of America

Sovereignty is held by
Democracy - the whole population (as a group)
Republic - the people (individuals)

Common confusion in the USA

Democracy - People commonly confuse direct democracy with representative democracy. The US officially has a representative style, though many have suggested the US is closer to an oligarchy or plutocracy.

Republic - The US is actually a Republic. It is governed by rule of law. The elected are bound by oath to the written governing limits (ie constitution) yet vote "together" and create laws to address concerns of the represented in a democratic way

Free Choice
Democracy - Individuals may make decisions for themselves except insofar as a majority faction has limited individuals.

Republic - Individuals may make decisions for themselves, especially insofar as there is a constitutional prohibition on interfering with freedom of choice.

Political System Democratic. [Note: this is not meant as a reference to a Democratic Party.] Republican. [Note: this is not meant as a reference to a Republican Party.]

Social Structure
Democracy - Class distinctions can become pronounced due to capitalist society. Varies from state to state.

Republic - Class distinctions can become pronounced due to capitalist society. Varies from state to state.

Religion
Democracy - Generally, freedom of religion is permitted, although a majority faction may limit religious freedom for a minority faction.

Republic - Generally, freedom of religion is permitted, especially insofar as there is a constitutional prohibition on interfering with freedom of religion.

Economic System
Democracy -Elected by the voters or their elected representatives. Usually capitalist or Keynesian.

Republic - Elected by the voters or their elected representatives. Usually capitalist or Keynesian.

Private Property
Democracy - Generally, private property is permitted, although a majority faction may place limits on property rights.

Republic - Generally, private property is permitted, especially insofar as there is a constitutional prohibition on interfering with property rights.

Discrimination
Democracy - In theory, all citizens have an equal say and so are treated equally. However, often allows for the tyranny of the majority over the minority.

Republic - In theory, all citizens have an equal say and so are treated equally by the government, especially insofar as there is a constitutional prohibition on government discrimination.

Variations
Democracy - Direct democracy, parliamentary democracy, representative democracy, presidential democracy.

Republic - Democratic republics, Constitutional republics.

Modern Examples
Democracy - More than half of the world, including the US, Canada, Western Europe, Australia, New Zealand, Japan, etc.

Republic - The United States of America is a republic.

Key Elements
Democracy - Free elections.
Republic - Free elections, constitution.

Way of Change
Democracy - Voting.
Republic - Voting.

Observation in practice
Democracy - People commonly confuse direct democracy with representative democracy. The US has a representative style. But the will of the people shouldnt easily decide to change the rules that limit power to the government.

Republic - The U.S.A.'s Constitution clearly shows the U.S. as a Republic, Article 4, Section 4 of the U.S. Constitution

Trump will bring back the United States the Republic
[link to www.diffen.com]