Childlike, childish agree in meaning having or showing the manner, spirit, or disposition of a child. Both are applicable to adolescents and to adults as well as to children.
Childlike, however, usually suggests such qualities of childhood as innocence, simplicity, or straightforwardness which are worthy of admiration or emulation; childish suggests such less pleasing and less admirable characteristics as helplessness, peevishness, or undeveloped mentality.