In those passages the Comforter (Holy Spirit -> God) would dwell in the people.
2 Cor 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 inthem; and I will be their God, and they shall be my people.
1 Cor 6:19 - What? know ye not that your body is the temple of the Holy Spiritwhich isin you, which ye have of God, and ye are not your own
There is only one identity being discussed here (in the temple).