We become sons of God by adoption. We become children of God by the new birth.
Being a son of God speaks of one's position in the family of God. Thus, even a female Christian can be called a son of God since this is a term which refers to one's spiritual position in the family. As a son of God, we have privileges and responsibilities to do. Being a child of God refers to our relationship with Him in the family.
Both happen at the same time, at the moment of faith. The very moment a sinner places his trust in Christ for salvation, he becomes, both, a son of God and a child of God.
