In Jeremiah 31:31-34 it says God said he'd make a new covenant that was not like the old one, but the new covenant had similarities to the old one.

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Jeremiah 31:31-34 is discussed at length in Hebrews 8-10. God is still God, morality remains the same, so it is to be expected that many features of any covenant established by God would contain similar characteristics. However, what Jeremiah is pointing out is that the new covenant would not be so close to the old one as to say that the new is just an extension of the old. There are many significant and fundamental differences between the two.

For example, the Old Covenant was only given to the nation of Israel. "And what great nation is there that has such statutes and righteous judgments as are in all this law which I set before you this day?" (Deuteronomy 4:8). The New Covenant was established for all people:

"Therefore remember that you, once Gentiles in the flesh--who are called Uncircumcision by what is called the Circumcision made in the flesh by hands -- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who once were far off have been brought near by the blood of Christ. For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. And He came and preached peace to you who were afar off and to those who were near. For through Him we both have access by one Spirit to the Father" (Ephesians 2:11-18).

The Old Covenant offered a hope of future salvation through the coming Messiah. The New Covenant offers salvation because the Messiah came and died for us. "But now He has obtained a more excellent ministry, inasmuch as He is also Mediator of a better covenant, which was established on better promises" (Hebrews 8:6).

Later the writer of Hebrews points out, "For the law, having a shadow of the good things to come, and not the very image of the things, can never with these same sacrifices, which they offer continually year by year, make those who approach perfect. For then would they not have ceased to be offered? For the worshipers, once purified, would have had no more consciousness of sins. But in those sacrifices there is a reminder of sins every year. For it is not possible that the blood of bulls and goats could take away sins" (Hebrews 10:1-4). That imperfect system of sacrifice for sin was replaced by a single, perfect sacrifice. "By that will we have been sanctified through the offering of the body of Jesus Christ once for all" (Hebrews 10:10). But it was a will that required a change in law because the Old Law did not have a provision for one perfect sacrifice. "Then He said, "Behold, I have come to do Your will, O God." He takes away the first that He may establish the second" (Hebrews 10:9).