The Preamable

The preamble is the clause in the contract that describes the parties.

'The people of the United States"  are the people who wrote the document.

"for the United States of America" is the organic republic formed by the Declaration of Independence.

The original constitution was untitled.   The United States (by act of congress) adopted the Constitution of the United States.   The people of the several states of the United States of America voted to adopt the "Constitution".  These are two documents adopted by two nations with two different jurisdictions.  One is civil law (US) and the other is common law (USA).