Hi Malcolm, glad the baptism entries helped.
The Relief Congregation wasn't formed by the Covenanters, although, like them, they broke from the main Presbyterian Church of Scotland.
There were many breakaway churches, usually known as Secessionist Churches because they seceded from the C of S.
It was all about the Patronage Act, passed in Queen Anne's reign, which gave the local Heritor's (landowners, nobility, local "big-shots") the right to chose the parish minister. This didn't go down at all well with many congregations. The parish of Hamilton for example, had as its principle Heritor, his grace the Duke of Hamilton, premier peer of Scotland and hereditary keeper of the palace of Holyroodhouse. A very high & mighty person who spent most of his time at Court in London. His choice of minister for the parish church in Hamilton (the only church in the entire parish) was someone as high-handed and intellectual as himself who preached way over the heads of the simple country folk of Hamilton. They would have been unable to understand his vocabulary and his views. This sort of thing happened in many parishes. In the neighbouring parish of Dalziel, the local landowner was the laird of Dalzell, (he was what was known as a "Bonnet Laird") a very ordinary, "home-grown" chap who had probably never been any further than Edinburgh in his life, so his choice of minister was quite acceptable to the parishioners. So Dalziel had no dissenting churches until the Disruption of 1843, when the Church of Scotland lost about one-third of its congregation. Hamilton and Cambusnethan (another parish with very rich gentry as Heritor's) both had Secessionist churches long before then.
The list of Secessionist groups is quite long - 1st Relief Congregation, United Congregation, Burgers, Antiburgers, Cameronians (Covenanters, also part of what was called The Reformed Presbyterian), Auld Lichts, New Lichts, United Associate Secession Church, Synod of Protesters, Original Secession Synod, Free Church, United Free Church.............
In 1843, Thomas Chalmers (1780 - 1847) minister in Glasgow (and later professor of moral philosophy at St Andrew's University and of Divinity at Edinburgh University) and 190 ministers & elders walked out of the General Assembly of the Church of Scotland and formed the Free Church. By 1847, there were 700 Free churches. In 1852, most of the members of the Constitutional Associate Church joined the Free Church.
In 1874 patronage was abolished by act of Parliament. Congregations were at last granted the right to elect their parish ministers.
In 1900 the Free Church united with the United Presbyterian Church to form the United Free Church, apart from 25 ministers and 63 congregations, mostly in the Highlands & Islands who stayed out of the union. Members of these churches became known as "Wee Frees".
In 1929, the United Free Church (apart from a small minority) united with the Church of Scotland.
Complicated? Yes it is! But it gives you an idea of the amount of church records apart from the original Church of Scotland ones, that are still out there. I do believe that the National Archives of Scotland are in the process of digitalising these records at the moment, so they will eventually be available online. Someone else will know much more about this than I do.
Here's a link
https://en.wikipedia.org/wiki/First_Secession