I have some background which may help explain the relationships.
Eliphalet & Betsey (GOODRICH) BEAN had 4 children that married VAUGHANs.
William Newman married Ruth VAUGHAN, the dgtr of Ira & Sarah (BOORN) VAUGHAN Edward F married Sarah B VAUGHAN, the dgtr of Ira & Sarah Hepzibeth married Alanson VAUGHAN, the son of Daniel & Content (BOORN) VAUGHAN Thomas Goodrich married Sarah VAUGHAN, the dgtr of Daniel & Content.
Sarah (BOORN) and Content (BOORN) were both dgtrs of Francis & Sarah (BECKWITH) BOORN
Thus, Ruth, Sarah, Alanson and Sarah were brother/sisters and cousins at the same time.
It is believed that Sarah, the dgtr of Ira & Sarah began using the name "Mary" in Wisconsin. Even your reference to her has these names together. The records in the Wisconsin Historical Society and other Wisconsin sources are the only place where these names are found together. I can imagine that having the three Sarahs all together at the same time in the same place must have been confusing. After all, this made Sarah VAUGHAN, the wife of Ira made her a mother/aunt to the collective BEAN spouses.
From the perspective of the BEAN family (and their descendants), the wife of Edward would have been Mary. From the perspective of the VAUGHAN family she would be Sarah B.
I have an extensive family genealogy website of the VAUGHANs of this line back to The Immigrant of the family. Please contact me off-line as I do not wish to post the URL on the Forum.
Good luck with your project.
As an aside, I am impressed that Corporal Edward BEAN belonged to the US Sharpshooters, arguably the most prestigious regiment that fought in the War Between the States. I have a picture of the medal he would have been awarded for his service. At 59 years old he must have been the "grandpa" in Company G. He must have been a living legend in Wisconsin. His wife, Mary-Sarah, would have been high-regarded herself.