The difference between the Old Covenant and the New Covenant is, as Woodznutz said, where the Law of God is written. Israel carried th Law in tablets of stone. True Christians carry God's Law with them, in their hearts
"True Christians carry God's Law with them, in their hearts"
I Disagree.
Mat 5:17
“Don’t think that I came to destroy the law or the prophets. I didn’t come to destroy, but to fulfill.
Mat 5:18 For most certainly, I tell you, until heaven and earth pass away, not even one smallest letter or one tiny pen stroke shall in any way pass away from the law, until all things are accomplished.
Mat 19:16 Behold, one came to him and said, “Good teacher,
what good thing shall I do, that I may have eternal life?”
Mat 19:17 He said to him, “Why do you call me good? No one is good but one, that is, God.
But if you want to enter into life, keep the commandments.”
Mat 19:18 He said to him, “Which ones?” Jesus said, “‘You shall not murder.’ ‘You shall not commit adultery.’ ‘You shall not steal.’ ‘You shall not offer false testimony.’
Mat 19:19 ‘Honor your father and your mother.’ And, ‘You shall love your neighbor as yourself.’”
Mat 19:20 The young man said to him, “All these things I have observed from my youth. What do I still lack?”
Mat 19:21 Jesus said to him, “If you want to be perfect, go, sell what you have, and give to the poor, and you will have treasure in heaven; and come, follow me.”
Exo 20:1 God spoke all these words, saying,
Exo 20:2 “I am Yahweh your God, who brought you out of the land of Egypt, out of the house of bondage.
Exo 20:3 “You shall have no other gods before me.
Exo 20:4 “You shall not make for yourselves an idol, nor any image of anything that is in the heavens above, or that is in the earth beneath, or that is in the water under the earth:
Exo 20:5 you shall not bow yourself down to them, nor serve them, for I, Yahweh your God, am a jealous God, visiting the iniquity of the fathers on the children, on the third and on the fourth generation of those who hate me,
Exo 20:6 and showing loving kindness to thousands of those who love me and keep my commandments.
Exo 20:7 “You shall not take the name of Yahweh your God in vain, for Yahweh will not hold him guiltless who takes his name in vain.
Exo 20:8 “Remember the Sabbath day, to keep it holy.
Exo 20:9 You shall labor six days, and do all your work,
Exo 20:10 but the seventh day is a Sabbath to Yahweh your God. You shall not do any work in it, you, nor your son, nor your daughter, your male servant, nor your female servant, nor your livestock, nor your stranger who is within your gates;
Exo 20:11 for in six days Yahweh made heaven and earth, the sea, and all that is in them, and rested the seventh day; therefore Yahweh blessed the Sabbath day, and made it holy.
Exo 20:12 “Honor your father and your mother, that your days may be long in the land which Yahweh your God gives you.
Exo 20:13 “You shall not murder.
Exo 20:14 “You shall not commit adultery.
Exo 20:15 “You shall not steal.
Exo 20:16 “You shall not give false testimony against your neighbor.
Exo 20:17 “You shall not covet your neighbor’s house. You shall not covet your neighbor’s wife, nor his male servant, nor his female servant, nor his ox, nor his donkey, nor anything that is your neighbor’s.”
Mat 22:34 But the Pharisees, when they heard that he had silenced the Sadducees, gathered themselves together.
Mat 22:35 One of them, a lawyer, asked him a question, testing him.
Mat 22:36
“Teacher, which is the greatest commandment in the law?”
Mat 22:37 Jesus said to him, “
‘You shall love the Lord your God with all your heart, with all your soul, and with all your mind.’
Mat 22:38
This is the first and great commandment.
Mat 22:39 A second likewise is this,
‘You shall love your neighbor as yourself.’
Mat 22:40
Jer 31:31 “Behold, the days come,” says Yahweh, “that
I will make a new covenant with the house of Israel, and with the house of Judah:
Jer 31:32
not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which covenant of mine they broke, although I was a husband to them,” says Yahweh.
Jer 31:33 “But this is the covenant that I will make with the house of Israel
after those days,” says Yahweh:
I will put my law in their inward parts, and I will write it in their heart. I will be their God, and they shall be my people.
Jer 31:34
They will no longer each teach his neighbor, and every man teach his brother, saying, ‘Know Yahweh;’ for they will all know me, from their least to their greatest,” says Yahweh: “for I will forgive their iniquity,
and I will remember their sin no more.” 
