Yes, the bible talks about two Israels. The first, which we can also call the ethnic Israel, is a picture and the foreshadow of the second, the Israel of God. All spiritual concepts of the NT have physical images given prior in the OT, allowing us to grasp their meaning. The people of God are no exception.
The nation of Israel was created by God as a rescue plan for the humanity. The bible teaches that the family of Jacob (70 members all together (Genesis 46:27)) down to Egypt and multiplied there. They were meant to be a kingdom of priests for the nations scattered after the tower of Babel event (70 nations all together, (Genesis 10)).
Immediately after the calling, the nation proved to be unfit for the task. The golden calf story shows us that Israel needed a major system upgrade to fulfil God's calling. That ecclesia was merely a shadow of the coming one (in LXX the OT Israel [the descendants of Jacob with the mixed multitude that left Egypt and later converts] are called ecclesia on numerous occasions).
Through the prophets we learn a plan, how that was going to happen. Isaiah 49 particularly shows us that the nation would be rebuilt and recentred around one individual, the messianic servant. The identity as an Israelite will be gained through faith in Jesus, regardless if one is a physical descendent of Jacob or not. That is why we were never told which tribes the twelve apostles came from. They represent the new twelve tribes of the spiritual Israel.
Being a Jew, contrary to the belief of the time, was not enough. Nicodemus was told that by Jesus in John 3. Being born of water, which meant being a descendant and/or a part of the people formed into the nation during the exodus (1 Corinthians 10:1-5), wasn't enough. To be a part of the kingdom of God, one needed an upgrade from above.
A person may be a Jew (ethnic Israelite) and an enemy of God and His people (Israel of God):
For you have heard of my previous way of life in Judaism, how
intensely I persecuted the church (ecclesia) of God and tried to
destroy it. (Galatians 1:13)
A person may be an uncircumcised gentile and be a seed of Abraham more than an unbelieving, genetic descendant:
28 A person is not a Jew who is one only outwardly, nor is
circumcision merely outward and physical. 29 No, a person is a Jew who
is one inwardly; and circumcision is circumcision of the heart, by the
Spirit, not by the written code. Such a person’s praise is not from
other people, but from God. (Romans 2)
2 Watch out for those dogs, those evildoers, those mutilators of the
flesh. 3 For it is we who are the circumcision, we who serve God by
his Spirit, who boast in Christ Jesus, and who put no confidence in
the flesh. (Philippians 3)
This mystery is foreshadowed in many places of the OT.
Jacob as a type of Christ had two wives. Leah had weak eyes (Genesis 29:17). She represents the physical Israel, who did not recognise their Messiah, and was loved less (Genesis 29:31). Rachel that he married after Leah was loved by him (Genesis 29:17). That is one of the verses John hyperlinked Revelation 3:9 to (the others are Isaiah 43:4; 45:14&60:14):
9 Look, I will force those who belong to Satan’s synagogue—those liars
who say they are Jews but are not—to come and bow down at your feet.
They will acknowledge that you are the ones I love.
Paul also wrote in Romans 1:
7 To all those in Rome who are loved by God and called to be saints:
The commandment concerning a concubine in Exodus 21 says:
7 ‘And when a man selleth his daughter for a handmaid, she doth not go
out according to the going out of the men-servants; 8 if evil in the
eyes of her lord, so that he hath not betrothed her, then he hath let
her be ransomed; to a strange people he hath not power to sell her, in
his dealing treacherously with her. 9 ‘And if to his son he betroth
her, according to the right of daughters he doth to her. 10 ‘If
another [woman] he take for him, her food, her covering, and her
habitation, he doth not withdraw; 11 and if these three he do not to
her, then she hath gone out for nought, without money.
The concubine represents the Israel according to the flesh that displeased God. Hence, He took another one, which is the spiritual Israel. Nevertheless, God is faith fool to his promises and has been preserving the unbelieving Jews for the last two thousand years.
In Romans 11:11-24, Paul talks about gentiles being grafted into the commonwealth of Israel of God through Jesus, the seed of Abraham. The idea comes from the careful reading of the promises given by God in Genesis 12:3 & 22:18.
I will bless those who bless you, and whoever curses you I will curse;
and all peoples on earth will be blessed through you.” (Genesis 12:3)
וַאֲבָֽרְכָה֙ מְבָ֣רְכֶ֔יךָ וּמְקַלֶּלְךָ֖ אָאֹ֑ר וְנִבְרְכ֣וּ בְךָ֔
כֹּ֖ל מִשְׁפְּחֹ֥ת הָאֲדָמָֽה׃
and through your seed all nations on earth will be blessed, because
you have obeyed me.” (Genesis 22:18) וְהִתְבָּרְכ֣וּ בְזַרְעֲךָ֔ כֹּ֖ל
גּוֹיֵ֣י הָאָ֑רֶץ עֵ֕קֶב אֲשֶׁ֥ר שָׁמַ֖עְתָּ בְּקֹלִֽי׃
Da'at Zekenim on Genesis 12:3:2 ונברכו בך כל משפחות האדמה, “and all
the families of the earth shall count themselves blessed if they can
establish family ties with you.” The root of the word ונברכו is the
same as that of מבריך, “to graft.” They will consider it an
accomplishment to have Abrahamitic blood in their veins.
Those rabbis almost got it right.
Jacob crossing his hands to bless and adopt Manasseh and Ephraim as his own sons is the foreshadow of the adoption of gentiles through the Messiah and his cross:
16 the Messenger who is redeeming me from all evil doth bless the
youths, and my name is called upon them, and the name of my fathers
Abraham and Isaac; and they increase (דָּגָה from the same root as
דָּג (fish)) into a multitude in the midst of the land.’ 17 And Joseph
seeth that his father setteth his right hand on the head of Ephraim,
and it is wrong in his eyes, and he supporteth the hand of his father
to turn it aside from off the head of Ephraim to the head of Manasseh;
18 and Joseph saith unto his father, ‘Not so, my father, for this [is]
the first-born; set thy right hand on his head.’ 19 And his father
refuseth, and saith, ‘I have known, my son, I have known; he also
becometh a people, and he also is great, and yet, his young brother is
greater than he, and his seed is the fulness of the nations/gentiles
(as in Romans 11:25);’