I agree with you all, but where do we find this most clearly articulated in Scripture?
I'll add the remarkably consistent theme from Genesis to Revelation: variations on "they will be my people and I will be their God."
Gen_17:8 And I will give unto thee, and to thy seed after thee, the land wherein thou art a stranger, all the land of Canaan, for an everlasting possession; and I will be their God.
Rev_21:3 And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
In between those bookends are at least 14 similar passages. Just a few samples:
Exo_29:45 And I will dwell among the children of Israel, and will be their God.
Jer_24:7 And I will give them an heart to know me, that I am the LORD: and they shall be my people, and I will be their God: for they shall return unto me with their whole heart.
Jer_32:38 And they shall be my people, and I will be their God:
Zec_8:8 And I will bring them, and they shall dwell in the midst of Jerusalem: and they shall be my people, and I will be their God, in truth and in righteousness.
2Co_6:16 And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
If God owns his people and is their God, and this is spoken by him in the future tense, then the two are necessarily, and eternally, distinct.