By: Jared Dalen
"The United States shall guarantee to every state in this UNION a
republican form of government, and shall protect each of THEM against
~Article IV, section 4 of the U.S. Constitution
These definitions are taken from Bouvier's Law Dictionary 1856:
STATE. government. This word is used in various senses. In its most
enlarged sense, it signifies a self-sufficient body of persons united
together in one community for the defence of their rights, and to do
right and justice to foreigners. In this sense, the state means the
whole people united into one body politic; (q. v.) and the state, and
the people of the state, are equivalent expressions. 1 Pet. Cond. Rep.
37 to 39; 3 Dall. 93; 2 Dall. 425; 2 Wilson's Lect. 120; Dane's Appx.
§50, p. 63 1 Story, Const. §361. In a more limited sense, the word
`state' expresses merely the positive or actual organization of the
legislative, or judicial powers; thus the actual government of the state
is designated by the name of the state; hence the expression, the state
has passed such a law, or prohibited such an act. State also means the
section of territory occupied by a state, as the state of Pennsylvania.
NATIONS. Nations or STATES are independent bodies politic; societies of
men united together for the purpose of promoting their mutual safety
and advantage by the joint efforts of their combined strength.
COUNTRY. By country is meant the STATE of which one is a member.
UNION. By this word is understood the United States of America.
Case law explaining the different contexts of the term "United States":
Hooven & Allison Co. v. Evatt, 324 U.S. 652 (1945): "The term
"United States" may be used in any one of several senses.  It may be
merely the name of a sovereign occupying the position analogous to that
of other sovereigns in the family of nations.  It may designate the
territory over which the sovereignty of the United States extends, or
 IT MAY BE THE COLLECTIVE NAME OF THE STATES WHICH ARE UNITED BY AND
UNDER THE CONSTITUTION."