I know this old but I'm sure someone else could use the answer later. We are told ignorance of the law is no excuse by the same people trying to hide the facts and make it as difficult as possible for us to understand. This will help anyone who needs it.
There is a difference. The "United States" refers to the Federal government, whilst the "United States of America" refers to the 50 States of the Union.
The legal definition for the United States of America; "The United States of America are a corporation endowed with the capacity to sue and be sued, to convey and receive property."
Courts have opined (3) legal meanings for the term "United States."
"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 to the United States  extends, or it may be the collective name of the states which are united by and under the Constitution."
None confirmed or legitimized by an act of Congress.
Furthermore, The United States of America is incorporated as 3 different Corporations. Twice in Delaware and once in Scotland.
The United States of America, Inc. and United States of America, Corp. are incorporated in Delaware.
The United States of America, Ltd. is a Limited Corp. incorporated in Scotland. The registration is held at White House #2 (sister White House) in Edinburgh. The country of origin for USA, ltd is U.K., which in my opinion confirms what I've suspected for a long time, we are still owned by Britain. (see original American flag "Grand Union Flag"). But that's a complicated
In short, wording is very important in regards to US law. Simple things like "are" or "is" can render an accepted perception of a meaning false. It's obvious Legislation intentionally creates vague and ambiguous terms to allow Courts headroom to conform the laws as needed, or rather desired (if law was all that mattered then legal meanings/definitions wouldn't vary by jurisdiction)
Some think the "United States" is a federal corporation, mainly because of Title 28 3002, which states, (15) United States means (A) a Federal corporation;
But that's specific only to that Chapter, not as an encompassing definition. The federal government has never been a federal corporation, plus the Supreme Court barred Congress from re-defining any terms used in the federal constitution anyway. But it should be amended for the unconstitutional nature as it stands now.
I know it seems overwhelming and complicated and if anyone rather just do simple I can't blame them. But if truth matters then the best way to research this (or similar) is by just starting with the knowledge of following facts;
There are (2) United States (US / USA), (2) Constitutions (the constitution / this Constitution), and (3) Presidential Offices (Office of President / President of the United States / President of the United States of America)
The actual "Office of President" has never been filled by anyone. The reason being, the Constitutional oaths are controlling factors of office.
Put simply, which oath 1 takes decides what office they fill. The oath taken by the 9th President, George Washington (only 1st under Constitutional scheme), was under Article II, (President of the United States), not (Office of President) which requires oath under Article VI. All Presidents have followed the same suit since.
That scheme against the people is why the Constitution was drafted in secret. (also why Washington was nervous taking oath) He knew he could likely be killed if caught. Patrick Henry's "I smell rat" was for good reason, yet he was ridiculed. But indeed he did. Same rat out of control today.
Whether anyone sees it or not, this info goes directly to the heart of the matter, the U.S. separated from U.S.A.. But once you dive in you'll see how quickly the pieces fall together and the dots start connecting.
You'll start to see the reason for all this trickery & deceit and what it basically comes down to. 1 giant ass tax & property theft scheme by the governments usurping of powers.
We're all just citizens subjected to a treasonous scheme and criminal trespass under guise & color of law.
America wasn't built, it merely spread.
-Cairo Anubiss (American Composer)