When you refer to an adult’s behaviour as being “childish”, what you mean is that he is behaving immaturely; he is behaving like a small child. The word has a negative connotation.
*The childish behaviour of the teacher had everyone in splits.
Unlike the word “childish”, the word “childlike” has a positive connotation. It means having some of the attractive qualities that one normally associates with a child — innocence, simplicity, and sincerity.
*Revathi took part in the activity with childlike enthusiasm.