The following Diagram of the Covenants is a simplified pictorial representation of the historical Baptist Covenant view.
(Diagram takes a minute to load into the placeholder at the foot of the page)
It is simplified in the following respects:
It is not an exhaustive representation of all God's Covenants (eg the Davidic and Solomonic and subsequent covenant statements are omitted as largely echoing and developing the ground of the Abrahamic and Mosaic covenants) but shows the sweep of the Old and New Covenants , and hopefully clarifies the notions of the Covenant of Grace and the Covenant of Works. Here is a link to a 3MB Acrobat.pdf download for A4 printing.
Scripture references have been omitted. This is purely a limitation of the clarity of the diagram, but the references are fully available in eg
The Divine Covenants by AW Pink (see on site link).
It is possible in such a simplification to inadvertently introduce errors or implications that are unintended and I would be very grateful to have these pointed out. The amillenial, non-restorationist view is deliberate (and I do not see a Jewish national restoration in Romans 11).
Unusually, John Gill, in most respects the greatest Baptist theologian, adopts the two administrations of one covenant view for the Old and New Covenants. John Owen, on the other hand, makes the case for the two separate covenants view. I have sympathy for John Gill's view as he expresses it, but I have been persuaded that Owen has the better case. I see the resolution briefly as follows:
There has only ever been one covenant leading to salvation - this has been and is, saving faith in the atoning work of the Lord Jesus Christ. All the Old Testament saints were saved by this faith, in their time it was in the promise of a Great Redeemer. The promise of Grace legally became a Covenant when its covenant terms were fulfilled by Christ's death, and it is in this respect that it is called the New Covenant..
The Old Covenant was the Sinaitic (aka the Mosaic) Covenant in which faultless obedience to the Law was the condition of salvation. Sacrificial atonements were available for some transgressions, but not all. The Law was a schoolmaster teaching the need of more righteousness than Man has, and hence the need for a Saviour Redeemer, a Righteousness provided by God. No one was saved by the terms of the Old Covenant! Any who were saved during the period of the Old Covenant were actually saved by the Promise of the Grace, which was active throughout the Old Covenant, and before it, right back to Genesis 3:15.
So, Salvation has always been by the Faith in the Redeemer, and in this sense Salvation in the OT can be rightly said to be by an administration of (actually by spiritual understanding of the Promise of) the Covenant of Grace. What John Owen says, is that there was a separate Old Covenant (as Hebrews 8.6), but that no-one was saved by that covenant. He is therefore correct to speak of two covenants with two different ends.
The potentially confusing issue is that salvation in the time of the Old Covenant was not by the terms of the Old Covenant, since the role of the Old Covenant was to drive men to the promises of Grace that were effective even at that time, and that would be fully revealed in the New Covenant.