They both refer to behaviors or attributes associated with children, but “childish” has a generally negative connotation and “childlike” has a generally positive connotation. e.g. “childish behavior” is usually something the author judges inappropriate, where “childlike wonder” is usually rendered as a positive (if often infantilizing) attribute. Similar definitions, but quite different in implication.
They both refer to behaviors or attributes associated with children, but “childish” has a generally negative connotation and “childlike” has a generally positive connotation. e.g. “childish behavior” is usually something the author judges inappropriate, where “childlike wonder” is usually rendered as a positive (if often infantilizing) attribute. Similar definitions, but quite different in implication.