From what I'm getting at, there are 3 definitions for the United States:

United States, in Congress Assembled; as in the federal government (Articles I, II, III, and VI in the Constitution).

United States, as in Washington D.C dba UNITED STATES, as well as it's extensions (see District of Columbia Organic Act of 1871; 28 USC 3002(15)(a); UCC 9-307(h); and 4 USC 110(d) and (e); AKA "Buck Act"; Article I, Section 8, Clause 17 of U.S Constitution).

United States, as in the 50 states of the Union that are independent of one another (see the Paris Peace Treaty of September 30, 1783; 28 USC 297(a) and (b); U.S Government Printing Office Style Manual; Preamble and Article IV, Sections 3 and 4 of the Constitution; Northwest Ordinance).

"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." - Hooven & Allison Co. v. Evatt, 324 U.S. 652 (1945)

If there's anything I missed let me know!