William Perkins has some good insights on the issue of the Sinai Covenant and how it is distinguished from the Covenant of Grace. His comments are taken from his commentary on Galatians 4:21-23:

Tell me, you who desire to be under the law, do you not hear the law? For it is written that Abraham had two sons: the one by a bondwoman, the other by a freewoman. But he who was of the bondwoman was born according to the flesh, and he of the freewoman through promise, which things are symbolic. For these are the two covenants...

Perkins writes,

The one, the one testament, which is the covenant of works, which testament is figured by Hagar came from Mount Sinai, where the law was delivered to the Israelites. And genders to bondage, that is, it makes all men bondmen that look to be justified and saved by the works of the law...

The two testaments are the Covenant of works, and the Covenant of grace, one promising life eternal to him that does all things contained in the law; the other to him that turns and believes in Christ. And it must be observed, that Paul says, they are two, that is, two in substance or kind. And they are two sundry ways.

1. The law, or covenant of works, propounds the bare justice of God, without mercy; the covenant of grace, or the gospel, reveals both the justice and mercy of God, or the justice of God giving place to his mercy.

2. Secondly, the law requires of us inward and perfect righteousness, both for nature and action; the Gospel propounds unto to us an imputed justice resident in the person of the Mediator.

3. Thirdly, the law promises life upon the condition of works; the gospel promises remission of sins and life everlasting, upon the condition that we rest ourselves on Christ by faith.

4. Fourthly, the law was written on tables of stone, the gospel in the fleshly tables of our heart, Jer. 31:33; 2 Cor. 3:3.

5. Fifthly, the law was in nature by creation; the Gospel is above nature, and was revealed after the fall.

6. Sixthly, the law has Moses for the mediator, Deut. 5:27; but Christ is the mediator of the New Testament, Heb. 8:6.

7. Lastly, the law was dedicated by the blood of beasts, Ex. 24:5, and the New Testament by the blood of Christ, Heb. 9:12.

Here then falls to the ground a main pillar in Popish religion, which is, that the law of Moses, and the Gospel are all one law for substance...

Here again Paul sets down two properties of the Testament [Covenant] of works, or of the law. The first is, that it came from Mount Sinai. And here lies the difference between the law and the gospel; the Law is from Sinai, the Gospel from Zion or Jerusalem...the second property of the law is that it genders bondage because it makes them bondmen that look to be saved and justified thereby. And this is done by revealing sin and the punishment thereof, which is everlasting death, and by convincing all men of their sins and of their deserved condemnation. In this respect, it is called the ministry of death, 2 Cor. 6; and Paul says that after he knew his sin by the law, he died, and the law was a means of death to him, Rom. 7:10.

William Perkins (1558-1602)