I’ve said it before and I’ll say it again: One of the coolest things about blogging is that you can put out some half-informed opinion on a topic you’re interested and actual experts will spend time educating you about it.
My old friend Jeremy Paretsky, who interrupted a career in comparative literature to enter the Dominican order as Fr. Albert and is now a scholar of, inter alia, New Testament Greek, writes in connection with my criticism of the phrasing “X is a testament to Y,” which I claimed should be “X is a testimony to Y”:
Greek-speaking Jews used διαθήκη (diatheke) (will, testament) to approximate the idea expressed by the Hebrew b’rith, though of course b’rith implies a bond established through treaty with obligations on both sides, whereas a will is a bond with the living that comes into effect through the death of the testator, important for development of Christian usage. The Vetus Latina relied on the Septuagint and translated διαθήκη as testamentum.
In the Vulgate Jerome translates b’rith as foedus, which underlies our English word federal, federation, but for the Christian scriptures translates διαθήκη as testamentum. At Luke 1:72 διαθήκη clearly means covenant , but Jerome translates as testamentum.
“New covenant,” as you point out, is derived from Jer 31:31ff. The term appears in 1 Cor 11:25, Luke 22:20, both usages in context of the cup at the Last Supper. (John 13:34 new commandment probably has Jer 31:31 in mind as well.) “New covenant” also is used in the quotation from Jeremiah at Heb 8:8.
Jerome translates all three usages as novum testamentum, even though he translates the Hebrew of Jer 31:31 as foedus novum . Heb 8:13 [ in speaking of a new covenant he treats the first as obsolete; and what is becoming obsolete and growing old is ready to vanish away ] is the source for supposing that the new covenant supersedes the old ; the argument is then drawn out in chapter 9.
The ambiguity of the word διαθήκη (will in standard Greek and covenant in Jewish Greek) allows the author of Hebrews to argue that the new covenant comes into effect with the death of Jesus (Heb 9:15-17, but see entire passage). The Latin novum testamentum and vetus testamentum, derived from this distinction, is behind the usage in the Latin church, so in western Europe.
In contemporary academic usage terms like first covenant and second covenant are used, or else Jewish Scriptures or Tanakh or Hebrew Bible and Christian writings or scriptures. There’s no agreed upon common term because until 1517 (or thereabouts) all European Christians used an old testament that was larger than the Hebrew Bible, though the writings were all Jewish. Now Christians don’t agree on what the content of the Old Testament is.
A footnote: I think that foedus gave us “feudal” as well as “federal.”