The covenant of grace. Salvation

“the word grace is used in scripture and in ordinary religion writings in three senses
1. For unmerited love; i.e; love exercised toward the undeserving.
2. For any unmerited favor, especially for spiritual blessings. Hence, all the fruit of the Spirit in believers are called graces, or unmerited gift of God.
3. The word grace often means the supernatural influence of the Holy Spirit. This is a preeminently grace, being being great gift secured by the work of Christ, and without which his redemption would not await to our salvation. In all these senses of the word and plan of salvation is properly called a covenant of grace. It is of grace because it originated in the mysterious love of God for sinners who deserve only His wrath and curse. Secondly, because it promises salvation not on the condition of works or anything mysterious on our part, but as an unmerited gift. And, thirdly, because it benefits are secured and applied not in the course of nature, or in the exercise of the natural power of the sinner, but by the supernatural influence of the Holy Spirit, granted to him as an unmerited gift.”
Charles Hodge: The covenant of grace.

The Parties

Sometimes Christ is present as one of the parties; at others He is presented not as a party, but as a mediator and surety of the covenant; while the parties are represented to be God and his people.
Christ is called the mediator of a better covenant founded on better promises.

Two Covenant’s

There are in fact two covenants relating to salvation of fallen man, the one between God and Christ, the other between God and his people. These covenants differ not only in their parties, but also in their promises and conditions. Both are so clearly presented in the Bible that they should not confounded. The latter is the covenant of grace, is founded on the former, the covenant of redemption. Of the one Christ is the mediator and surety; of the other ( redemption ) He is one of the contracting parties.

To Covenant To Be Distinguished

This confusion is avoided by distinguishing between the covenant of redemption between the a father and the Son, and the covenant of grace between God and and His people. The later supposes the former, and is founded apron it.
They differ as to the parties, the promises, and the conditions.

The Covenant of Redemption

The covenant between the Father and the Son in reference to the salvation of man.