According to the web document it is the same family. Walton County Georgia was named after George Walton who signed the Declaration of Independence and served as Governor of the state of Georgia. He was raised by his Uncle, also named George, who is the person named in the title of the document.

See the second sentence of page 1 for the following note:

"General Notes: GUARDIAN TO THE MINOR CHILDREN OF HIS BROTHER, ROBERT, including GEORGE (Signer of the
Declaration of Independence)."