The Bishops Transcript (BT) differed from the Parish Register. Each year every parish had to submit a copy of all the entries in the parish register to the Bishop of the diocese. Sometimes the copy differed from the PR, either by mistake or by the vicar taking the opportunity to correct an error he'd spotted in the PR.
So the name of the baptised was either William, or perhaps John, and his mother was Mary, or perhaps Elizabeth.
You'd need to check other baptisms at around that time to see if it was more likely to have been John and Elizabeth rather than John and Mary as the parents. As it's a double change I tend to think the vicar may have realised the original was in error. You can only usually tell from the context - was there already a son named William or John, who hadn't been buried in the meantime?
Regards
David
PS Just remembered I've got that fiche as well! I'm not so sure that the BT isn't doubly wrong! Look at the previous entry where the copier had also made a mess of the entry, also Elizabeth/Mary. Other baptisms around that time were all John and Mary Wilmot, and included a John baptised in 1767, for whom there is no burial so on the face of it he was still alive in 1769, when William/John was baptised.
On balance I think I would go with the PR, rather than the BT
