That makes you wrong.
When I read Eph 2:12-15 I see a new Israel that includes all believers.
It's not a "new Israel."
It's just the Remnant! The portion of Israel who was NOT cut off for its unbelief!
The problem with calling them "new Israel" is that God isn't done with the unbelieving portion of Israel! Paul makes that extremely clear in Romans 9-11!
Just READ those three chapters!
Paul starts out chapter 9 (not that there were any chapters to begin with) by stating, almost explicitly, that he's not talking about the Body of Christ, and then explains that aside from the believing portion of Israel (which He calls "Israel," AKA "the Remnant"), there is also those who are "of Israel" (the unbelieving portion) that are not Israel. He then talks about Israel's rejection of her Messiah (Christ) and their present condition, that they, pursuing the law, have not attained righteousness, in contrast to the Gentiles who did not pursue the law having attained it by faith, why? Because Israel did not seek righteousness by faith, but by works of the law.
He then points out that they do have a zeal for God, but that their zeal for Him through the law is what prevents them from attaining righteousness through faith. "For Christ is the end of the law for righteousness to everyone who believes."
Paul then gets into the differences between "the righteousness which is of the law" and "the righteousness which is of faith, pointing out that the law requires a man to live according to a standard, whereas faith is keeping the word of faith near to you, in your mouth and in your heart, "that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved." This is in direct opposition to what Moses wrote!
Anyways, Paul then explains that Israel rejects the gospel of faith (because of their adherence to the law and to their own good works), and presents the fact that God has been waiting for them to repent, but they, having heard the gospel, and know it, and even having Christ who is God manifest Himself to them, they still disobey Him, and it was for that reason that God cut them (Unbelieving Israel) off.
Does that then mean that Israel has been cast away? "CERTAINLY NOT!" as Paul says. "God has not cast away His people whom He foreknew. Or do you not know what the Scripture says of Elijah, how he pleads with God against Israel, saying,“ Lord, they have killed Your prophets and torn down Your altars, and I alone am left, and they seek my life” ?But what does the divine response say to him? “I have reserved for Myself seven thousand men who have not bowed the knee to Baal.”Even so then, at this present time there is a remnant according to the election of grace.And if by grace, then it is no longer of works; otherwise grace is no longer grace. But if it is of works, it is no longer grace; otherwise work is no longer work."
"What then? Israel has not obtained what it seeks; but the elect have obtained it, and the rest were blinded."
The "Elect" here is still Israel, the Remnant. (see verse 5). Paul didn't just suddenly start talking about the Body of Christ, no, he's still talking about Israel.
Israel's rejection is not final. He says: "have they stumbled that they should fall? Certainly not! But through their fall, to provoke them to jealousy, salvation has come to the Gentiles.Now if their fall is riches for the world, and their failure riches for the Gentiles, how much more their fullness!For I speak to you Gentiles; inasmuch as I am an apostle to the Gentiles, I magnify my ministry,if by any means I may provoke to jealousy those who are my flesh and save some of them.For if their being cast away is the reconciling of the world, what will their acceptance be but life from the dead?For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches.And if some of the branches were broken off, and you, being a wild olive tree, were grafted in among them, and with them became a partaker of the root and fatness of the olive tree,do not boast against the branches. But if you do boast, remember that you do not support the root, but the root supports you.You will say then, “Branches were broken off that I might be grafted in.”Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear.For if God did not spare the natural branches, He may not spare you either.Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off.And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again.For if you were cut out of the olive tree which is wild by nature, and were grafted contrary to nature into a cultivated olive tree, how much more will these, who are natural branches, be grafted into their own olive tree?"
Paul then writes: I say then, have they stumbled that they should fall? Certainly not! But through their fall, to provoke them to jealousy, salvation has come to the Gentiles.Now if their fall is riches for the world, and their failure riches for the Gentiles, how much more their fullness!For I speak to you Gentiles; inasmuch as I am an apostle to the Gentiles, I magnify my ministry,if by any means I may provoke to jealousy those who are my flesh and save some of them.For if their being cast away is the reconciling of the world, what will their acceptance be but life from the dead?For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches.And if some of the branches were broken off, and you, being a wild olive tree, were grafted in among them, and with them became a partaker of the root and fatness of the olive tree,do not boast against the branches. But if you do boast, remember that you do not support the root, but the root supports you.You will say then, “Branches were broken off that I might be grafted in.”Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear.For if God did not spare the natural branches, He may not spare you either.Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off.And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again.For if you were cut out of the olive tree which is wild by nature, and were grafted contrary to nature into a cultivated olive tree, how much more will these, who are natural branches, be grafted into their own olive tree?
Paul then finishes by saying this, which you should read carefully:
For I do not desire, brethren, that you should be ignorant of this mystery, lest you should be wise in your own opinion, that blindness in part has happened to Israel until the fullness of the Gentiles has come in.And so all Israel will be saved, as it is written: “The Deliverer will come out of Zion, And He will turn away ungodliness from Jacob;For this is My covenant with them, When I take away their sins.”Concerning the gospel they are enemies for your sake, but concerning the election they are beloved for the sake of the fathers.For the gifts and the calling of God are irrevocable.For as you were once disobedient to God, yet have now obtained mercy through their disobedience,even so these also have now been disobedient, that through the mercy shown you they also may obtain mercy.For God has committed them all to disobedience, that He might have mercy on all.Oh, the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments and His ways past finding out!“For who has known the mind of the Lord? Or who has become His counselor?”“Or who has first given to Him And it shall be repaid to him?”For of Him and through Him and to Him are all things, to whom be glory forever. Amen. - Romans 11:25-36
http://www.biblegateway.com/passage/?search=Romans11:25-36&version=NKJV
It is written..."That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
13 But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
14 For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us;
15 Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;"
You need to read the whole passage, not just a portion of it:
Therefore remember that
you, once
Gentiles in the flesh—
who are called Uncircumcision by what is called the Circumcision made in the flesh by hands—that at that time
you were without Christ, being aliens from the
commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world.But now in Christ Jesus
you who once were far off have been brought near by the blood of Christ.For He Himself is our peace, who has made both one, and has broken down the middle wall of separation,having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace,and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity.And He came and preached peace to you who were afar off and to those who were near.For through Him we both have access by one Spirit to the Father. - Ephesians 2:11-18
http://www.biblegateway.com/passage/?search=Ephesians2:11-18&version=NKJV
Paul here is talking about breaking down the (quite superficial, yet also very important, but only under the law) distinction between Jew and Gentile.
For you are all sons of God through faith in Christ Jesus.For as many of you as were baptized into Christ have put on Christ.There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise. - Galatians 3:26-29
http://www.biblegateway.com/passage/?search=Galatians3:26-29&version=NKJV
Note that He said "Abraham's seed" and not "Isaac's seed."
Do not lie to one another, since you have put off the old man with his deeds,and have put on the new man who is renewed in knowledge according to the image of Him who created him,where there is neither Greek nor Jew, circumcised nor uncircumcised, barbarian, Scythian, slave nor free, but Christ is all and in all. - Colossians 3:9-11
http://www.biblegateway.com/passage/?search=Colossians3:9-11&version=NKJV
Note that ONLY in the "new man" (an organism, not a nation) is there no difference.
The old Israel still doesn't believe and is not part of those in Christ.
The "old Israel" you're referring to is not "old Israel" nor is it a different nation. It's still Israel. It's the portion of Israel that was cut off for their unbelief, but that will be grafted back in again later.
Agreed, if you are referring to the country and not those in Christ.
I meant what I said.
They are not the same thing just with different names.
Israel is a country, a nation. The Body of Christ is an organism, a new man. They are two distinct entities.
Shall we now call the believing Jews "Gentiles"?
No.
Under the New Covenant, prior to Paul's conversion, believing Jews were still Israel.
Under the dispensation of grace, after Paul's conversion and to this very day, anyone who believes is neither Jew nor Gentile, as I quoted Paul above.
Maybe we should come up with our own name for those in Christ that includes both Jew and Gentile?
No need.
I know..."The body of Christ"!
Do not lie to one another, since you have put off the old man with his deeds,and have put on the new man who is renewed in knowledge according to the image of Him who created him,where there is neither Greek nor Jew, circumcised nor uncircumcised, barbarian, Scythian, slave nor free, but Christ is all and in all. - Colossians 3:9-11
http://www.biblegateway.com/passage/?search=Colossians3:9-11&version=NKJV
He may as well have said "believers and unbelievers".
That would have only brought more confusion, because of the fact that there are two relevant dispensations, in which "believer and "unbeliever" mean different things.
But what about the cross-overs?
There are none.
As Paul said:
Circumcision is nothing and uncircumcision is nothing, but keeping the commandments of God is what matters.
Let each one remain in the same calling in which he was called.Were you called while a slave? Do not be concerned about it; but if you can be made free, rather use it.For he who is called in the Lord while a slave is the Lord’s freedman. Likewise he who is called while free is Christ’s slave.You were bought at a price; do not become slaves of men.Brethren, let each one remain with God in that state in which he was called. - 1 Corinthians 7:19-24
http://www.biblegateway.com/passage/?search=1Corinthians7:19-24&version=NKJV
The Gentiles in the body of Christ and the Jews in the body of Christ.
What is it about "no distinction between Jew and Greek" do you not understand?
Again:
For you are all sons of God through faith in Christ Jesus.For as many of you as were baptized into Christ have put on Christ.There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise. - Galatians 3:26-29
http://www.biblegateway.com/passage/?search=Galatians3:26-29&version=NKJV
Perhaps a third entity entirely?
There's only two groups, as far as "the people of God" are concerned: the nation of Israel, and the Body of Christ.
The new Israel is certainly different from the old, unbelieving Israel.
There's only Israel, which contained both believers and unbelievers, but now is a nation cut off from her God until the fullness of the Gentiles comes in. Her dispensation of the New Covenant is NOT currently in effect, and there are NO members of it alive today.
One has turned from sin and been baptized into Christ and the other hasn't.
Once again you conflate Paul's dispensation of grace with the covenant of law.
The New Covenant wasn't about being "baptized into Christ." It was about believing that Christ was the Messiah.
I know which one I have been made one with.
Confusion reigns in you.