The Westminster Standards use “Covenant of Grace” and “New Covenant” interchangeably

Compare WLC 162 with WSC 92.

Q. 162. What is a sacrament?

A. A sacrament is an holy ordinance instituted by Christ in his church, to signify, seal, and exhibit unto those that are within the *covenant of grace*, the benefits of his mediation; to strengthen and increase their faith, and all other graces; to oblige them to obedience; to testify and cherish their love and communion one with another; and to distinguish them from those that are without.

Quest. 92. What is a sacrament?

Ans. 92. A sacrament is an holy ordinance instituted by Christ, wherein, by sensible signs, Christ, and the benefits of the *new covenant*, are represented, sealed, and applied to believers.(1)

(1) Gen. 17:7, 10; Exod. 12; I Cor. 11:23, 26.

WLC 166

Of God’s Covenant with Man
Chapter 7 Westminster Confession of Faith.

Section IV.—This covenant of grace is frequently set forth in the Scripture by the name of a testament, in reference to the death of Jesus Christ, the testator, and to the everlasting inheritance, with all things belonging to it, therein bequeathed.

Section V.—This covenant was differently administered in the time of the law, and in the time of the gospel: under the law it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all fore-signifying Christ to come, which were for that time sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation, and is called the Old Testament.

Section VI.—Under the gospel, when Christ the substance was exhibited, the ordinances in which this covenant is dispensed, are the preaching of the Word, and the administration of the sacraments of Baptism and the Lord’s Supper; which, though fewer in number, and administered with more simplicity and less outward glory, yet in them it is held forth in more fullness, evidence, and spiritual efficacy, to all nations, both Jews and Gentiles; and is called the New Testament. There are not, therefore, two covenants of grace differing in substance, but one and the same under various dispensations.

The OPC website uses the term: ‘new covenant of grace‘

“Under the new covenant of grace man was to receive a greater degree of blessing than that which the Old Testament saints received. These blessings were not to be of an entirely different kind from those experienced under the Old Testament dispensation. They were essentially the same kind of blessings but showered forth in greater abundance and in a higher degree (see Heb. 8:6–11).

Under the new covenant of grace man received a clearer and fuller revelation of grace than that received by the Old Testament saints.”

“The New Covenant is taken either broadly or strictly.

V The New covenant is also taken in a twofold manner either broadly, inasmuch as it stands for the covenant of grace in general made with sinners , which existed under the Old Testament as well before Christ appeared as under the New after he had been manifested; or strictly, for the covenant of grace promulgated after the manifestation of Christ in the flesh, which should continue to the end of the World”

Francis Turretin, Institutes of Elenctic Theology Vol 2, pg 234

C. Hodge seems to take the same route:

“As Christ is a party to the Covenant of redemption, so he is constantly represented as the mediator of the covenant of grace; not only in the sense of an internuncius, as Moses was a mediator between God and the people of Israel, but in the sense (1) that it was through his intervention, and solely on the ground of what He had done, or promised to do, that God entered into this *new covenant* with fallen man” (My emphasis added)

Systematic Theology, C. Hodge, pg 364

“Israel’s captain general is here described by his relation to them: Thy God; The Lord thy God. This relation is stated upon the ground of a new covenant dispensation, even a covenant of promise in Christ Jesus. Of this covenant there was an Old-Testament dispensation, under which this people of Israel were; and a New-Testament dispensation, under which we are. The former was a darker, and this is a clearer and brighter dispensation of the same new covenant. The old covenant of works being broken and violated by the sin of man, God could not in honour come under this relation again to sinners but upon the ground of a new covenant established in Christ. This covenant of promise was first discovered to Adam in Paradise, afterwards to Abraham and others. The promise of that new covenant was sealed by the blood of Christ, typically, under the Old Testament, by the sacrifices then offered; and actually at Jerusalem, when he gave his life a ransom for many.”

The reverend Daniel Hyde writes:

“When our Lord Jesus Christ was born, lived, died, and was raised from the grave, the covenant of grace reached its zenith in what the Bible calls “the new covenant” (Jer. 31:31; Luke 22:20; 1 Cor. 11:25; 2 Cor. 3:6; Heb. 8:8, 13; 9:15; 12:24). Under the covenant of grace, Christ accomplished what Adam failed to do in the covenant of works, so we receive grace:”

Francis Turretin writes:
“The New Covenant is taken either broadly or strictly. V The New covenant is also taken in a twofold manner either broadly, inasmuch as it stands for the covenant of grace in general made with sinners , which existed under the Old Testament as well before Christ appeared as under the New after he had been manifested; or strictly, for the covenant of grace promulgated after the manifestation of Christ in the flesh, which should continue to the end of the World”