“Childish” and Childlike”, although often used synonymously, are subtly different.
Childish refers to characteristics of a child that are not endearing, not pleasing, and not desirable. Characteristics like selfishness, temper tantrums, and whining. Spoiled brats, regardless of age, are childish.
Childlike refers to characteristics of a child that are endearing, pleasing, and desirable. Characteristics like innocence, honesty, and trusting. Children of God, regardless of age, are childlike (Matt 19:13-14).