I'm not familiar with Ripon registers, but what you've come across sounds similar to what I've seen with larger West Riding parishes such as Bradford and Halifax where there are a number of townships, each with its own church.
I've been doing quite a bit of research on my ancestors who lived in and around Ripon. I've noticed that when I search Yorkshire parish registers for Ripon on FindMyPast I often get two records for the same individual with different archive references. Checking the images shows that these are two different documents. Can anyone enlighten me as to whether these are actual PR entries, later transcriptions, or BTs, and how I can identify which is which?....
Also, does an entry for Ripon Cathedral actually mean that? I have relatives who lived in villages around Ripon that had their own churches, Bishop Monkton, for example, but PR entries for some individuals who lived there have entries for Ripon Cathedral when I would have expected them to be for their local church.
The township churches generally became parishes in their own right, but before that, and sometimes afterwards too, events in the township churches were often duplicated in the mother church's registers. Add to that the Bishops Transcripts, and sometimes rough copies of the register or day books, and there can be multiple copies to be found.
Without seeing the documents in question, I can't say exactly what you've found, but if you look at the website's transcription rather than the document itself, you might find something to tell you what it is. The documents themselves also sometimes contain clues: for example, each year of the BTs is usually on a separate sheet, with the vicar and churchwardens' signatures at the bottom, whereas register entries run continuously through the book.
For the Ripon area, though, if the documents you've find are all from FindMyPast, I think they will be registers rather than BTs - but I'd advise you to check this rather than rely on me. Most of the BTs for Yorkshire are kept at the Borthwick Institute, and they are at FindMyPast, but the ones for the Richmond Archdeaconry (which includes Ripon) are at West Yorkshire Archives in Leeds. Since WYAS has an agreement with Ancestry, I think those BTs will be at Ancestry rather than FindMyPast.
Then, some PR records for around the mid 1600s for a marriage have the marriage performed by the vicar then described as "Major of Ripon". What does this signify?
And again, why were the "publication of the agreements exercised in the forenoon on the Lords Dayes"? I'm assuming this is the equivalent of publishing the Banns?
Again, without seeing the documents I can't be certain, but this sounds like the way marriages took place during the Commonwealth period - and "Major" might actually be "Mayor".
The Commonwealth lasted from 1642 to 1660, and between 1653 and 1660 keeping registers was the responsibility of the civil authorities rather than the church, and marriage was a civil affair rather than a church ceremony. I've seen references to it taking place before a magistrate, but it may be that in different places, different officials were involved.
Hope that helps.