The only thing there might be a difference on is the terms. The new convenant was established by Christ:
Heb 12:24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than [that of] Abel.
He affirmed the covenant at the last supper:
Mat 26:28 For this is My blood of the new covenant, which is shed for many for the remission of sins.
I agree though that it could just as well be thought of a renewal because God's promises never changed...but he actually did add on to his promises by now adding in eternal life, which wasn't in the old covenant.
But as far as the law it's exactly right...nothing in the law changed except that which was specified in scripture. Israel broke the original covenanat, not God.
God in his mercy made it in a sense easier for us to fulfill the terms by giving us the gift of his holy spirit to live in and through us and enable us to grow in righteousness. With the sacrifice of Christ it no longer became about us trying to keep the law...it became about Christ indwelling in us and living through us to do so and covering our sins while we grow in faith. The outward appearance is that we are keeping the written law. This is how I believe the law is written on our hearts.
Mat 26:28 For this is My blood of the new covenant, which is shed for many for the remission of sins.
I think not. Think about the following verses.
Matthew 26:
26 And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body.
27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;
28 For this is my blood of the new testament, which is shed for many for the remission of sins.
One of the Noahide laws, carried over into Mosaic, is the commandment to abstain from 'drinking blood'. Jesus was a devout Jew, righteous. Do you really think that Jesus would suggest something, say something like the above verses, knowing full well that it was against Torah????
More likely the drinking of blood was added later. Drinking of blood is pagan, and probably introduced by Paul, whose roots were pagan Tarsus.
To suggest 'eating his flesh', canibalism, too, I would think Jesus would have been horrified at the idea, much less say something so ungodly.
The catholic eucharist believes that the wine and wafer become the actual body and blood of Christ. Do you have any idea how many people were burned at the stake because they refused to accept this pagan idea??
In my opinion, Jesus would NEVER had said such a thing. So WHO inserted it?
Since Paul's writings are the oldest in the NT, it seems logical that the gospels were crafted to support Paul's gospel, of gnostic paganism. jmo
Acts 15
19 Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
20 But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood.
21 For Moses of old time hath in every city them that preach him, being read in the synagogues every sabbath day.
Acts 15
28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things;
29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well.
30 So when they were dismissed, they came to Antioch: and when they had gathered the multitude together, they delivered the epistle:
Genesis 9
3 Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.
4 But flesh with the life thereof, which is the blood thereof, shall ye not eat.