In the new covenant Christian and child of God are synonamous
One must be born of God to be his child (tekna)
John 1:12 (KJV)
12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Ok.... but can one be a child of God and NOT be a Christian? I say absolutely. There are many children of God who fail to become Christians and will suffer for their failure.