Both mean the same thing. It is all about Jesus. The New Testament is about the new covenant and the gift of the Holy Spirit.
The New Testament is a Will, the New Covenant is a contract that God will make w/ the house of Israel, & the house of Judah in the future. Gentiles aren't mentioned anywhere in the book of Hebrews, so either the writer of Hebrews made a mistake (which I'm sure you wouldn't suggest), or it was a wrong translation of the Greek word in the newer translations in Paul's epistles.
Promise of Restoration
Ezekiel 11:16-20
Therefore say, Thus saith the Lord GOD; Although I have cast them far off among the heathen, and although I have scattered them among the countries, yet will I be to them as a little sanctuary in the countries where they shall come.
Therefore say, Thus saith the Lord GOD; I will even gather you from the people, and assemble you out of the countries where ye have been scattered, and I will give you the land of Israel.
And they shall come thither, and they shall take away all the detestable things thereof and all the abominations thereof from thence.
And I will give them one heart, and I will put a new spirit within you; and I will take the stony heart out of their flesh, and will give them an heart of flesh:
That they may walk in my statutes, and keep mine ordinances, and do them: and they shall be my people, and I will be their God.
Israel To Be Renewed For His Name's Sake
Ezekiel 36:22-28
Therefore say unto the house of Israel, Thus saith the Lord GOD; I do not
this for your sakes, O house of Israel, but for mine holy name's sake, which ye have profaned among the heathen, whither ye went.
And I will sanctify my great name, which was profaned among the heathen, which ye have profaned in the midst of them; and the heathen shall know that I
am the LORD, saith the Lord GOD, when I shall be sanctified in you before their eyes.
For I will take you from among the heathen, and gather you out of all countries, and will bring you into your own land.
Then will I sprinkle clean water upon you, and ye shall be clean: from all your filthiness, and from all your idols, will I cleanse you.
A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do
them.
And ye shall dwell in the land that I gave to your fathers; and ye shall be my people, and I will be your God.
A New Covenant
Jeremiah 31:31-34
Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Not according to the covenant that I made with their fathers in the day
that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:
But this
shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
A New Covenant (cf Jeremiah 31:31-34)
Hebrews 7:8-12
For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.