These two signatures come from marriage bonds in Nicholas County, Kentucky. The person of interest, Agusta Newman, whose signature is underlined, is not the groom in either of the documents. He serves a purpose in each record, but any specific familial relationship between Newman and the individuals getting married or the other individuals listed in the records is not stated.
The signature underlined in red comes from an 1829 marriage permission that Agusta witnesses for Sophia Thomas to her "Sun William A. Thomas." The signature underlined in green comes from an 1830 marriage bond that Agusta and Richard Harding sign for the impending marriage of Richard Harding and Mrs. Sophia Thomas.
Agusta's relationship to the individuals is not stated.
One could speculate that Sophia is widowed in 1830 and Agusta is signing the marriage bond and apparently vouching for Sophia's eligibility to be married. The widowhood of Sophia at the time of the marriage is speculation--there's nothing to indicate she was widowed. What's clear is that she was single before the marriage. Since Harding (the groom) signs the bond with Agusta, it would be reasonable to conclude that Agusta had knowledge of Sophia's ability to marry.
Agusta also witnessed Sophia's consent given in 1829 for her "Sun" to marry.
What's clear is that Agusta had a relationship to Sophia. Just what that relationship is is not stated in the documents.
If I had been uncertain that this Agusta Newman of Nicholas County, Kentucky, was the same one who later lived in White County, Indiana, a comparison of signatures of both men would have been in order.
Agusta's signatures in Kentucky were obtained in records that are not even "technically" about him--he's not getting married. Agusta apppears in land and property tax records in the Nicholas County, area, but those records do not include his signature.
Agusta's signatures when he lived in White County, Indiana, were obtained from his bounty land application and his surrendered military warrant. Both of those files are at the National Archives.
Records we need are not always in the immediate area where we are researching and they are not always "about" the actual person of interest.