This science of the similitudes between the two Testaments is called typology.
And here we would do well to remind ourselves of its foundation, for this is to be found in the Old Testament itself.
At the time of the Captivity, the prophets announced to the people of Israel that in the future God would perform for their benefit deeds analogous to, and even greater than those He had performed in the past.
So there would be a new Deluge, in which the sinful world would be annihilated, and a few men, a “remnant,” would be preserved to inaugurate a new humanity;
there would be a new Exodus in which, by His power, God would set mankind free from its bondage to idols; there would be a new Paradise into which God would introduce the people He had redeemed.
These prophecies constitute a primary typology that might be called eschatological, for the prophets saw these future events as happening at the end of time.
The New Testament, therefore, did not invent typology, but simply showed that it was fulfilled in the person of Jesus of Nazareth. With Jesus, in fact, these events of the end, of the fullness of time, are now accomplished.
He is the New Adam with whom the time of the Paradise of the future has begun. In Him is already realized that destruction of the sinful world of which the Flood was the figure. In Him is accomplished the true Exodus which delivers the people of God from the tyranny of the demon.
Typology was used in the preaching of the apostles as an argument to establish the truth of their message, by showing that Christ continues and goes beyond the Old Testament: “Now all these things happened to them as a type and, they were written for our correction” (I Cor. 10, 11). This is what St. Paul calls the consolatio Scripturarum (Rom. 15, 4).
But these eschatological times are not only those of the life of Jesus, but of the Church as well. Consequently, the eschatological typology of the Old Testament is accomplished not only in the person of Christ, but also in the Church.
Besides Christological typology, therefore, there exists a sacramental typology, and we find it in the New Testament. The Gospel of St. John shows us that the manna was a figure of the Eucharist; the first Epistle of St. Paul to the Corinthians that the crossing of the Red Sea was a figure of Baptism; the first Epistle of St. Peter that the Flood was also a figure of Baptism.
Jean Daniélou, S.J. (1905 – 1974): The Bible and the Liturgy, Liturgical Studies, 3 (Notre Dame, IN: University of Notre Dame Press, 1956), pp. 1-2.