I never really bothered to look up the meaning of the old testament and the new testament in regard to the naming of the books of the Bible before and after Jesus.
(KJV) For this is my blood of the new testament, which is shed for many for the remission of sins.
(ESV,NASB) For this is my blood of the covenant, which is poured out for many for the forgiveness of sins.
So in any case, here’s the Greek for the pertinent words:
New — G2537 — καινός — kainos — kahee-nos’
Of uncertain affinity; new (especially in freshness; while G3501 is properly so with respect to age): – new.
Testament — G1242 — διαθήκη — diathēkē — dee-ath-ay’-kay
From G1303; properly a disposition, that is, (specifically) a contract (especially a devisory will): – covenant, testament.
Shed — G1632 — ἐκχέω, ἐκχύνω — ekcheō ekchunō — ek-kheh’-o, ek-khoo’-no
From G1537 and χέω cheō (to pour); to pour forth; figuratively to bestow: – gush (pour) out, run greedily (out), shed (abroad, forth), spill.
Remission — G859 — ἄφεσις — aphesis — af’-es-is
From G863; freedom; (figuratively) pardon: – deliverance, forgiveness, liberty, remission.
Sins — G266 — ἁμαρτία — hamartia — ham-ar-tee’-ah
From G264; sin (properly abstract): – offence, sin (-ful).
Sins is from G264 — ἁμαρτάνω — hamartanō — ham-ar-tan’-o
Perhaps from G1 (as a negative particle) and the base of G3313; properly to miss the mark (and so not share in the prize), that is, (figuratively) to err, especially (morally) to sin: – for your faults, offend, sin, trespass.
Which is consistent with Romans 3:23 “for all [a]have sinned and fall short of the glory of God,”
Basically, just straight forward insight in what Jesus was actually doing by coming by the will of the Father and dying. The old covenant is fulfilled and the new covenant is here, through Jesus’ blood sacrifice as all humans sin and are not perfect like God.
edit: As I go through the New Testament it’s very interesting to see how consistent the ideas, themes, and fundamental points of Christianity are even between multiple authors. I suppose that’s why it is said the Scriptures are inspired by God.