KiwiRose,
With the Church of Ireland their records are public records and so are probably the most easily accessible, in terms of copying. With the Roman Catholic church it’s really up to the bishops to decide about access, and that can be granted en bloc for all parishes. But with Presbyterian churches, the records are not public documents and they belong to each congregation. So one congregation may agree to allow access and another may not.
I have no idea how Emerald Ancestors obtained their records for Ballyeaston 2nd. I suspect it was probably from the originals rather than PRONI’s copy, but you would need to ask them to get the facts. It may just be that the 2nd Congregation agreed to allow EA to copy them when the 1st did not.
PRONI generally have microfilmed copies and the originals are still held by the church. There are some exceptions to that, notably if a church has closed. There are some originals in PRONI and some in the Presbyterian Historical Society in Belfast. It all rather depends on what the congregation decided to do with their records. PRONI’s copy for Ballyeaston 1st is a microfilm copy, not the original.
Some Presbyterian churches have put their baptism & marriage records on CDs and sell them. (Donegore 1st springs to mind in this respect). But it’s up to each congregation to decide. One congregation may have an enthusiastic committee eager to raise money by providing this service, and another may not. If you write to the Minister for assistance, especially with a simple enquiry, some will reply with helpful answers and some will ignore your letter. It sounds as though what you hope to do is a trawling search. Most Ministers haven’t the time to do that, which is why I think you may need a researcher to do it for you.
There are also theological reasons why some Presbyterian congregations are reluctant to allow commercial and other organisations to copy their records but we’ll leave that for another day.