The volunteers at my FHC tell me the AF is about 75% accurate. That means the other 25% isn't. I've seen some real howlers in it, including a fellow who married and sired 5 children, starting 23 years AFTER he died. It looked to me like the Ohio George Prior on the AF matched up to the Ohio George P. whose service records wewe on Ancestry - the cavalry sargent.
It was a common name. There were 30+ George Priors and about 7 George W. Priors in the list from "Civil War Soldiers".You may have discovered yet another flaw in the 140-yeard old records. Your GP from Vermont was in a different unit from the one who deserted.