The Cov. of Redemption is inter-Trinitarian. Sometimes called the
pactum salutis. It is the eternal decision/determination to effect the Father's plan of Redemption, through the Son's voluntary sacrifice.
The New Covenant is the covenant age of the Messiah's triumph. It is the latest administration of the Covenant of Grace.
The covenant of Grace not completely the same as the Cov. of Redemption. The Sum of Saving Knowledge (not part of the WCF, but often appended) explicitly affirms the separate nature of the CoR. However, the CoR and CoG are tightly interconnected.
WLC Question 31: With whom was the covenant of grace made?
Answer: The covenant of grace was made with Christ as the second Adam, and in him with all the elect as his seed.
This Q/A orients the believer toward heaven, where looking as it were through the Robe of his Redeemer, he observes the eternal covenant enacted. The CoG is the outworking of the CoR in its spatio-temporal aspect. The reason the question refers to the CoG is precisely because of the second clause which includes his seed.
If we only were to consider the first clause of the answer, and to speak of the agreement of the Son with the Father to assume all his Mediatorial roles, to the glory of the Triune God (thus excluding from the discussion subsidiary parties of interest, i.e. mankind), then it should have been called the CoR. But the catechism is entirely taken up with the question of the provision and application of Redemption to the beneficiaries--namely, us. Therefore, it is appropriate to call the whole schema by a name for our participatory aspect.
The New Covenant is made between Christ and the same elect people that all the other CoG administrations have been made between, relative to their place in the history of Redemption.
Saints before the cross were members of the CoG. The New Covenant has more obvious qualities in common with the Abrahamic administration than the Mosaic administration, primarily because of the the added elements of the Law under Moses. These elements served their purpose, and according to Gal., have been set aside.
However, under Moses there was no essential change to the essence of the Abrahamic administration, even as certain legal additions were made. Because the Law coming 430 years after could not affect the promise. So, all that earlier remained in effect. And now, the main difference is that promise has become reality.
So, it is anachronistic to speak of saints before Christ as being "within the NC." It is preferable to speak of them as being in the CoG, and thus sharing with us after the cross all the same basic benefits.
Heb 11:39-40 "And these all, having obtained a good report through faith, received not the promise: God having provided some better thing for us, that they without us should not be made perfect."
For example, the earlier saints did not experience the outpouring of the HS. They experienced his new-birth, but they were not all indwelt in the manner of New Covenant believers. So, the same, and yet different.
