To put it much less formally than curiousdannii's excellent long and informative response.
The defining difference is indeed the Incarnation, but this is not only "an event" but marks a foundational difference in both the content and how it is perceived.
Between the two - many centuries of perceived "silence" - at least by the Jewish people of the day.
What does “in persona Christi Capitis” mean?
In persona Christi Capitis is a Latin phrase meaning "in the person of Christ the Head of the Church”, an important concept in Catholicism. A priest acts in persona Christi, because he acts as in the place of Christ. The term, In persona Christi capitis, “in the person of Christ the head of the Church,” was ...
There's a little bit of history to the titles Old Testament and New Testament that needs to be explained.
We begin with the Greek word διαθήκη (diatheke) which has two major distinct sub-senses and cannot be translated with a single English word.
a last will and testament
a compact/contract/covenant, and in this sense it was used to translate בְּרִית (...
It means: "in the person of Christ the Head [of the Church]".
Christ is the High Priest, in Whose person all other ordained priests act when they offer the Holy Sacrifice of the Mass.
When a Catholic priest consecrates the host and wine, he truly identifies Himself with Christ when he says "This is my body." and "This is my blood."
St. Robert Bellarmine ...