Biblical Understanding based on the Record of Scripture
When YHVH refers to the people of God (My people) He is referring to a relationship based on sins being covered. With Israel, that was the Old Covenant. When the reference though is to the children of God (the family of God) the relationship is based on the forgiveness of sin. That is the new Covenant. Many scriptures have been misinterpreted based on those relationships not being understood. Whether the relationship is with a people or in the context of a family tells us what covenant is being addressed.