One might think these are one and the same, but they aren’t.
A “child of God” refers to the New Testament description of a Christian, a
person who has received new life and adoption into God’s family through
salvation. The “people of God” refers to the Old Testament Israelites. Being
called a child of God is open to all who believe, regardless of race, status,
age, gender, etc. Only the Israelites could be called “the people of God”. What
is the difference in how these two groups act?