The Different Interpretations of Judaism and Israel in Comparison with Catholicism and the Catholic Church

• Abrogationist Supersessionism views Judaism as completely ended. Thus, Christianity is an entirely new faith, with no continuity between the faiths, such as the shared Revelation of the Old Testament.

• Fulfillment Supersessionism views Christianity as supplementing Judaism. It has replaced some aspects of Mosaic Judaism, such as animal sacrifice. But there is nevertheless a valued continuity between the faiths, such as the shared Revelation of the Old Testament.

• Dual Covenantism is the opposite to Supersessionism. It is the view that the Jєωιѕн covenant remains salvific for Jews. It claims that there are two routes to salvation: Old Covenant Judaism for Jєωιѕн peoples and New Covenant Christianity for others.

• Mosaic Covenant vs the New Covenant

Hebrews 8:13 - In speaking of “a new covenant,” he has made the first one obsolete. And what is obsolete and growing old will soon disappear.

https://catholicstand.com/did-vatican-ii-change-the-doctrine-of-supersessionism/

MYSTICI CORPORIS CHRISTI
ENCYCLICAL OF POPE PIUS XII
June 29, 1943

29. And first of all, by the death of our Redeemer, the New Testament took the place of the Old Law which had been abolished; then the Law of Christ together with its mysteries, enactments, institutions, and sacred rites was ratified for the whole world in the blood of Jesus Christ. For, while our Divine Savior was preaching in a restricted area - He was not sent but to the sheep that were lost of the House of Israel [30] - the Law and the Gospel were together in force; [31] but on the gibbet of His death Jesus made void the Law with its decrees [32] fastened the handwriting of the Old Testament to the Cross, [33] establishing the New Testament in His blood shed for the whole human race.[34] "To such an extent, then," says St. Leo the Great, speaking of the Cross of our Lord, "was there effected a transfer from the Law to the Gospel, from the ѕуηαgσgυє to the Church, from the many sacrifices to one Victim, that, as Our Lord expired, that mystical veil which shut off the innermost part of the temple and its sacred secret was rent violently from top to bottom."