This post is rather old, but the names fit the father of the John Bays, Jr. that is the center of a collaborative process being worked on now.
Now that I have looked at the referenced WikiTree profile for William Bays (Bays-30), his father is Peter Bays (and wife Sarah Bibb) who is also the father of John Bays, Sr. who married Elizabeth Bannister. So, yes, that makes William and John brothers.
I saw all these names on the open shared tree on FamilySearch and they are a seriously confused mess. Since I am mainly concerned with John Bays, Jr. in our present project, there may be a need to address his father and grandfather in order to sort things out and try to reduce the confusion on WikiTree. If and when that happens, the results will spill over to their profiles here on WT.