The New Covenant and the New Testament are two different things. We disagree, obviously.
Grace and peace, covenantee.
Are these verses referring to two different things? I don't believe so.
Hebrews 7:22 By so much was Jesus made a surety of
a better testament.
Hebrews 8:6 But now hath he obtained a more excellent ministry, by how much also he is the mediator of
a better covenant, which was established upon better promises.
The words "testament" and "covenant" in these veress are translated from the same Greek word ""diathéké", so the decision by the KJV translators to translate the Greek word differently in each verse is highly questionable. In the NKJV, the Greek word is translated as "covenant" in Hebrews 7:22 instead of testament, so it is more consistent.
The following passage indicates that both the new covenant and new testament went into effect upon the death of Christ...
Hebrews 9:15 And for this reason
He is the Mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant, that those who are called may receive the promise of the eternal inheritance. 16
For where there is a testament, there must also of necessity be the death of the testator. 17 For a testament is in force after men are dead, since it has no power at all while the testator lives. 18
Therefore not even the first covenant was dedicated without blood.
This is from the NKJV. It's worth noting again that the words "covenant" and "testament" in this passage are both translated from the same Greek word "diathéké". In the KJV the Greek word is translated as "testament" every time it's used in this passage, so at least it's consistent even though I would say that the word should have been translated as "covenant" in each verse instead. Why the NKJV translators translated that word as both "covenant" and "testament" within this passage is a bit of a mystery since it indicates that both the new covenant and the new testament were put into effect by the death of Christ.
In this passage it indicates the Jesus became the Mediator of the new covenant by way of His death and it also implies that the new testament was in force by way of His death since it explains that a testament is only in force after the death of the testator (Jesus, in this case). And it is explained that the first covenant (the old covenant) was not in force without blood (the death of a sacrificed animal). So, the words covenant and testament seem to be used interchangeably as synonyms in this passage, which is why the English translators apparently had trouble deciding which English word the Greek word should be translated to in each verse that it was used. The words covenant and testament don't mean the same thing in English, but the Greek word that was translated as both "covenant" and "testament" seems to mean the same thing in each of the above verses and others that refer to the new covenant or new testament.