In another thread, Dr. Bob described his church as
I know the definitions Particular Baptist and Reformed Baptist, but I'm not sure what non-covenantal (or covenantal) means.
So, rather than derail the other thread, I simply ask for definitions and how they relate to Baptist congregations.
In Reformed theology there are two major covenants: the Covenant of Works and the Covenant of Grace (sometimes called the Covenant of Redemption). The CoW applied only to Adam. Adam, pre-fall, would have been justified by his obedience to God's law had he never sinned. Of course Adam did sin and consequently became a covenant breaker.
The CoG was promised in the Old Testament and realized after Christ's resurrection. It will be perfected in the eternal state.
There are other covenants that fall under the auspices of both covenants. Some say that the Old Covenant was a republication of the Covenant of Works in that the Old Covenant could never save. The Abrahamic Covenant was actually rooted in the Covenant of Grace. The Davidic Covenant pointed towards the coming Messiah. The New Covenant was made between Christ and His elect from all time.
Baptist systematic theology was not fully vetted among Calvinistic Baptists in the 16th and 17th centuries. English Particular Baptists were more concerned about legitimatizing their existence as opposed to English Presbyterians who questioned their legitimacy.
Most of the scholarly work on Baptist Covenant Theology was done in the later half of the 20th and into the 21st centuries. It is not that Baptist Covenant Theology did not exist before these times, it is just that it was not of primary importance. The importance grew when many Particular Baptists rejected what John Nelson Darby was doing with his Dispensational Theology in the mid-19th century.
Most Reformed Baptist churches that subscribe to the 1689 London Baptist Confession of Faith are more likely (but not exclusively) to be covenantal.
A good resource is
The Distinctiveness of Baptist Covenant Theology by Pascal Denault.