The Political Spectrum
Foundation of United States Government
Article 4 – The States
Section 4 – Republican Government
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
Republic
republic n 1 : a government having a chief of state who is not a monarch and is usually a president; also : a nation or other political unit having such a government 2 : a government in which supreme power is held by the citizens entitled to vote and is exercised by elected officers and representatives governing according to law; also : a nation or other political unit having such a form of government Source: NMW
In the context of the United States, both definitions apply.