The Jane McFarland group included a marriage bond for her marriage to Allen McFarland, three census records (1910-1930), a photograph of her headstone (obtained from my wife's cousin, Diana Moss-Clark), and a memorial for her on Findagrave.com. The marriage record is the only one that mentions her maiden name of Thacker. No in-laws, siblings, parents, or other relatives appear in the censuses; it's just her and her kids (and her husband in 1910). Her headstone simply gives her name, Jane McFarland, birth and death dates, and the inscriptions "MOTHER" and "Asleep in Jesus". The Findagrave memorial is likewise brief - it transcribes the birth and death dates and the inscription of "Mother", and gives the headstone's location as Indian Creek Cemetery, Anderson County, Tennessee.
The Jane Thacker/Patterson group included one census (1900), death certificates for Prior Patterson and Jannie Patterson, and a series of emails from Sharp's Funeral Home. The census lists Jane as the daughter of Samuel and Margaret Thacker, living in Roane County, Tennessee, with Jane's siblings and step-siblings. It also gives her birthdate as June 1891. All these details match very well with the death certificate for Jannie Patterson. The death certificates for Prior and Jannie establish their marriage, though they don't help in determining when that marriage took place. Jannie's death certificate states she was buried in Cove Cemetery, Oliver Springs, Tennessee, which is where Prior Patterson was buried, according to his death certificate. And, as it turns out, Oliver Springs is pretty unique town - it is simultaneously part of three counties - Morgan, Anderson and Roane.
As far as I could tell, nothing in group A overtly conflicted with anything in group B. But neither was there a "smoking gun" - a document that explicitly linked Jane McFarland to Jane Thacker/Patterson. But one thing that helped me make the decision on whether these two women were the same person was the series of emails I mentioned. Jannie's death certificate said that her undertaker was Sharp's Funeral Home in Oliver Springs. A quick Google search led me to the Sharp's Funeral Home website, complete with contact information! I sent them a short email asking if they had any information on whether the Jannie Patterson they provided funeral services for could be the same person as Jane McFarland, and whether Indian Creek Cemetery was also known as Cove Cemetery. Ninety minutes later (yes, that fast!) I had a response! They did not have any funeral records on Jane McFarland, but they did show Jannie Patterson as being buried in the Indian Creek Cemetery. They also said that Indian Creek Cemetery was also known as Indian Creek Baptist Church Cemetery, Cove Cemetery, and the Cove Road Cemetery. This meant that Prior Patterson and Jane Thacker/Patterson were buried in the same cemetery as Jane McFarland.
So, while I still don't have that smoking gun, I think I have enough evidence to make a conclusion. Given the location of burial for Jane and Prior; the coincidence of Jane's birth and death dates between census records, the death certificate, and the headstone; and the lack of significant conflicts between the data in these records, I have concluded that Jane McFarland and Jane Thacker/Patterson are the same individual.