"Childish", to me, means immature, and usually describes behavior or thought. "Childlike" means resembling a child in some way, or resembling something a child does. An adult crying because they've been criticized by their boss at work is childish, but not childlike. A fashion model wearing pigtails and dressed in a schoolgirl's outfit might be childlike, but not childish. A game that is usually played by children is childish, but not childlike. Handwriting or painting could be either childish or childlike.