Federalists are people who were in favor of the Constitution, and Anti-Federalists were against the Constitution. This pertains to when the Constitution was first being introduced, after the Articles of Confederation were abolished.
Federalist are people who a person who advocates or supports a system of government in which several states unite under a central authority. While Anti Federalist are a person who opposed the ratification of the Constitution in 1789 and thereafter allied with Thomas Jefferson's Antifederal Party, which opposed extension of the powers of the federal Government.
