I just read a commentary on the three types of people who represent the seed of Abraham. The author likened them to the Jews, the Arabs, and the Church. I’ve only recognized these Scriptures to be speaking to two groups; the “earthly promises” to Israel and the “heavenly/spiritual promises” to the Church. Would you please clarify.
Like you, I have an opinion that differs somewhat from the commentary you’re quoting.
In Genesis 13:16 God said He would make Abraham’s descendants like the dust of the earth. This promise was made in conjunction with showing Abraham the Promised Land and refers to the Jews.
In Genesis 16:10 the Angel of the Lord promised Hagar that her descendants (through Ishmael) would be too numerous to count, but made no reference to sand, dust, or stars.
In Genesis 22:17 God told Abraham his descendants would be as numerous as the stars in the sky and the sand on the seashore. This was said just after the interrupted sacrifice of Isaac, which was a model of the sacrifice of Jesus, and was meant to show how all nations would be blessed because of Abraham.
I believe the stars in the sky was a reference to the redeemed Church (in Christ we are Abraham’s seed according to Galatians 3:29 and come from every nation) dwelling in the New Jerusalem above Earth, and the sand on the seashore points to Israel in the Millennium, when they will finally recognize the Messiah and dwell in the Land on Earth.