Difference Between "United States" and "United States of America" for Declarations

Title 28 U.S. Code § 1746 can be used to learn that… United States and United States of America, are Two Different Entities.
…there is a Republic and Democracy going on at the same time…
 the United States of America is the Republic jurisdiction…
and the United States is in the DC/District of Columbia democracy jurisdiction.

Title 28 1746 Federal Rules of Evidence

The difference between "United States" and "United States of America" is expressly written in 28 USC § 1746 (1) which shows that whenever "United States of America" is used for a declaration there is a reservation of specific rights that is not offered by 'default' when this term is not used. See the law's details below:

https://www.law.cornell.edu/uscode/text/28/1746

28 U.S. Code § 1746 - Unsworn declarations under penalty of per­jury
Wherever, under any law of the United States or under any rule, regulation, order, or requirement made pursuant to law, any matter is required or permitted to be supported, evidenced, established, or proved by the sworn declaration, verification, certificate, statement, oath, or affidavit, in writing of the person making the same (other than a deposition, or an oath of office, or an oath required to be taken before a specified official other than a notary public), such matter may, with like force and effect, be supported, evidenced, established, or proved by the unsworn declaration, certificate, verification, or statement, in writing of such person which is subscribed by him, as true under penalty of perjury, and dated, in substantially the following form:

(1) If executed without the United States: “I declare (or certify, verify, or state) under penalty of perjury under the laws of the United States of America that the foregoing is true and correct. Executed on (date).
(Signature)”.

(2) If executed within the United States, its territories, possessions, or commonwealths: “I declare (or certify, verify, or state) under penalty of perjury that the foregoing is true and correct. Executed on (date).
(Signature)”.