There are several factions within the Messianic community, but those tht believe in Jesus are more commonly known as "Messianic" as far as I am familiar.
"Jew" is representative of the " house of Judah", led by the tribe of Judah after Jacob's (Israel's) son. There were also bits and pieces of the other tribes by marriage and the house of Benjamin that were associated with the house of Judah which split with the house of Israel - the northern territory of Israel. The house of Israel and its 10 tribes rebelled against the King of Judah and split in civil war, just as God said they would do, and after a succession of evil kings, were carried off into captivity by Assyria many years before the house of Judah was taken into captivity by Babylon and carried off. The house of Judah would return, though, and bebuild the temple that Jesus visited in His life.
The covenant to Abraham was that from his seed he would become the father of many "hamon goyim" or (noisy) Gentile nations. Those are represented by the "house of Israel" which is the 10 tribes that were torn away from the inheritance of David because Solomon married so many foreign wives and allowed their baal -asheroth worship in Israel. Ephraim, the son of Joseph born in Egypt was the head of the lost sheep of the house of Israel that God said He would sift into the Gentile nations but not ever lose track of (Amos 9:9). Through Hosea (1:9-12), God told us that at a later date they would come forth once again in history as "Sons of the Living God" and reunite with their brother in the house of Judah. Ephraim was called and given the rights as the "firstborn of God" (Jer.3:19), and that should give us a good clue as to who the house of Israel and the house of Judah are today in history. The Church today is even referred to as the "Church of the firstborn" in Hebrews 12:23. This new revelation of God's covenant is to the house of Judah and the house of Israel according to Hebrews 8:6-10 and the day is coming when these two houses will be reunited under one King who was from the tribe of Judah - Jesus. Jacob's blessing to Judah was that the sceptre of headship would never pass from him (Gen. 49:10), but the firstborn rights went to Ephraim and Mannaseh with Ephraim going before.. It was through Ephraim and the house of Israel that the huge numbers of multilicity desribed in God's covenant with Abraham as, "stars in the sky" and "sands of the sea" would be reached. Not through just the two tribes of people in the house of Judah from where we get the term Jews - those descendants of the house of Judah who returned from captivity to rebuild the temple where Jesus came saying - "I am not sent but unto the lost sheep of the house of Israel" (Matt. 15:24). Jesus said He came to call this house out of the Gentile nations and said they would hear and follow His voice (John 10:16). The Bible is actually very careful in distinguishing between the two houses of Israel, but often, theologians have ran the two together and failed to see the seperate roles that they would play in coming together in God's plan for the end times and reunion
So, from the begining, God has had a plan to make all people elligible as God's chosen people and family, but not just through the Jews, but also through the house of Israel inside the Gentile nations where they would become a particularly powerful nation that would come to the aid of their brother Judah in the last days, as Isaiah and the prophets foretold . It was said by the prophets that this nation or nations would "possess the gates of their enemies" and have the fat of the land to live on but would forsake their faith in the end and come under judgment by God once again. The alien lands once again, as once was before, would rise up and bring judgment upon them for unbelief. Micah speaks of this in chapter 5 saying that their tall images would be knocked down and that their cities filed with sorery would be destroyed as early judgments. before the great tribulation of days. As in the former days of Israel being judged, when Israel and Judah were carried off into captivity by their enemies, history tries to repeat itself, but It won't happen again, though, as a remnant of both houses will live because of the abiding faith living within them by God's Holy Spirit. They will see the Lord's return and restoration of all things on the earth for a last final day of 1000 years - the millinnium
Throughout the Old Testament, te prophets speak of the reunion of the two witnesses to the God of Abraham, Isaac, and Jacob. Few acknowledge this, but a second exodus has happened by those Sons of the Living God coming out of the Gentile nations to once again put aside their differences with their brother, Judah. Together, they will become the family of God along with their companions - the grafted in branches Paul speaks of in his letter to Romans.
Isa 11:11 And it shall come to pass in that day, that the Lord shall set his hand again the second time to recover the remnant of his people, which shall be left, from Assyria, and from Egypt, and from Pathros, and from Cush, and from Elam, and from Shinar, and from Hamath, and from the islands of the sea. 12 And he shall set up an ensign for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth. 13 The envy also of Ephraim shall depart, and the adversaries of Judah shall be cut off: Ephraim shall not envy Judah, and Judah shall not vex Ephraim. 14 But they shall fly upon the shoulders of the Philistines toward the west; they shall spoil them of the east together: they shall lay their hand upon Edom and Moab; and the children of Ammon shall obey them.
JER 23:7-8 Therefore behold, the days are coming," declares the Lord, "when they will no longer say, ‘As the Lord lives, who brought up the sons of Israel from the land of Egypt,’ but, ‘As the Lord lives, who brought up and led back the descendants of the household of Israel from the north land and from all the countries where I had driven them.’ Then they will live on their own soil.
EZE 39:27-28 When I bring them back from the peoples and gather them from the lands of their enemies, then I shall be sanctified through them in the sight of the many nations. Then they will know that I am the Lord their God because I made them go into exile among the nations, and then gathered them again to their own land; and I will leave none of them there any longer.
Jer 3:18 In those days the house of Judah will walk with the house of Israel, and they will come together from the land of the north to the land that I gave your fathers as an inheritance.
Zech.9:13 When I have bent Judah for me, filled the bow with Ephraim, and raised up thy sons, O Zion, against thy sons, O Greece, and made thee as the sword of a mighty man. 14 And the LORD shall be seen over them, and his arrow shall go forth as the lightning: and the Lord GOD shall blow the trumpet, and shall go with whirlwinds of the south.
Amos 9:9 "For surely I will command, And will sift the house of Israel among all nations, As grain is sifted in a sieve; Yet not the smallest grain shall fall to the ground.
Judah's sceptre:
Ge 49:10 The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be.
Ephraim's promise:
Gen. 48:18 And Joseph said unto his father, Not so, my father: for this is the firstborn; put thy right hand upon his head.
19 And his father refused, and said, I know it, my son, I know it: he also shall become a people, and he also shall be great: but truly his younger brother shall be greater than he, and his seed shall become a multitude of nations.
20 And he blessed them that day, saying, In thee shall Israel bless, saying, God make thee as Ephraim and as Manasseh: and he set Ephraim before Manasseh.
Jeremiah 31:9 They shall come with weeping, and with supplications will I lead them: I will cause them to walk by the rivers of waters in a straight way, wherein they shall not stumble: for I am a father to Israel, and Ephraim is my firstborn.
Hebrews 12:23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect,
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.
7 For if that first covenant had been faultless, then should no place have been sought for the second.
8 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:
9 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.
10 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:
11 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.
12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.
Hosea 1:9 Then God said: "Call his name Lo-Ammi, For you are not My people, And I will not be your God.
10 "Yet the number of the children of Israel Shall be as the sand of the sea, Which cannot be measured or numbered. And it shall come to pass In the place where it was said to them, ‘You are not My people,’ There it shall be said to them, ‘You are sons of the living God.’
11 Then shall the children of Judah and the children of Israel be gathered together, and appoint themselves one head, and they shall come up out of the land: for great shall be the day of Jezreel.
