Old testament -old covenant
New testament- new, better covenant
just saying what the NWT states, so that's a difference
31 “Look! The days are coming,” declares Jehovah, “when I will make with the house of Israel and with the house of Judah a new covenant.+ 32 It will not be like the covenant that I made with their forefathers on the day I took hold of their hand to lead them out of the land of Egypt,+ ‘my covenant that they broke,+although I was their true master,’* declares Jehovah.”33 “For this is the covenant that I will make with the house of Israel after those days,” declares Jehovah. “I will put my law within them,+ and in their heart I will write it.+ And I will become their God, and they will become my people.”+34 “And they will no longer teach each one his neighbor and each one his brother, saying, ‘Know Jehovah!’+ for they will all know me, from the least to the greatest of them,”+ declares Jehovah. “For I will forgive their error, and I will no longer remember their sin.”+
3 For you are shown to be a letter of Christ written by us as ministers,+ inscribed not with ink but with the spirit of a living God, not on stone tablets+but on fleshly tablets, on hearts.+4 We have this sort of confidence toward God through the Christ. 5 Not that we of ourselves are adequately qualified to consider that anything comes from us, but our being adequately qualified comes from God,+ 6 who has indeed adequately qualified us to be ministers of a new covenant,+ not of a written code,+ but of spirit; for the written code condemns to death,+but the spirit makes alive.+
6 But now Jesus has obtained a more excellent ministry* because he is also the mediator+ of a correspondingly better covenant,+ which has been legally established on better promises.+7 If that first covenant had been faultless, there would have been no need for a second.+ 8 For he does find fault with the people when he says: “‘Look! The days are coming,’ says Jehovah,* ‘when I will make with the house of Israel and with the house of Judah a new covenant. 9 It will not be like the covenant that I made with their forefathers on the day I took hold of their hand to lead them out of the land of Egypt,+ because they did not remain in my covenant, so I stopped caring for them,’ says Jehovah.*10 “‘For this is the covenant that I will make with the house of Israel after those days,’ says Jehovah.* ‘I will put my laws in their mind, and in their hearts I will write them.+ And I will become their God, and they will become my people.+
