The United States of America is a federal constitutional republic.
A republic is:
a. A political order in which the supreme power lies in a body of citizens who are entitled to vote for officers and representatives responsible to them.
b. A nation that has such a political order.
Democracy is a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections.
Federalism is a political concept in which a group of members are bound together by covenant (Latin: foedus, covenant) with a governing representative head. The term "federalism" is also used to describe a system of the government in which sovereignty is constitutionally divided between a central governing authority and constituent political units (like states or provinces). Federalism is a system based on democratic rules and institutions in which the power to govern is shared between national and provincial/state governments, creating what is often called a federation.
In modern republics such as the United States and India, the executive is legitimized both by a constitution and by popular suffrage. Montesquieu included both democracies, where all the people have a share in rule, and aristocracies or oligarchies, where only some of the people rule, as republican forms of government.
Charles-Louis de Secondat, baron de La Brède et de Montesquieu (18 January 1689 – 10 February 1755), generally referred to as simply Montesquieu, was a French social commentator and political thinker who lived during the Enlightenment. He is famous for his articulation of the theory of separation of powers, taken for granted in modern discussions of government and implemented in many constitutions throughout the world. He was largely responsible for the popularization of the term feudalism.
A constitution is:
a. The system of fundamental laws and principles that prescribes the nature, functions, and limits of a government or another institution.
b. The document in which such a system is recorded.
c. Constitution The fundamental law of the United States, framed in 1787, ratified in 1789, and variously amended since then.