Yes. Childish implies that someone is immature. They are thinking or behaving like a child, but they should be thinking or behaving like an adult. Childlike means "as a child would do" without any judgment attached.

These are similar but are not used as synonyms. Childish is almost always used negatively. So, if an adult man is not taking his responsibilities serious, he might be referred to as being 'childish', meaning he is displaying the traits of a child in a way that is negative reflection of his character. Childlike is generally used to indicate that someone is like a child in the way they perceive the world. So, if you go on vacation with a new friend and you notice that they see a whale for the first time and they are in awe of the whale, you might say that they, "watched the whale with childlike awe". This can alse be used when someone is naive or overly trusting, you might say "I worry that this man is going to take advantage of my sister because she trusts everyone, she has a childlike belief in the goodness of all people." So, Childish is a negative attribution of someone's personality because they are not as mature or responsible as they should be. And childlike, while still somewhat negative, is less of an accusation against their character because it tends to come from a position of trusting and naivity.

Childish is always used negatively towards anyone who is behaving in a manner like a child throwing a tantrum. Or simply not facing up to the consequences of their actions, behaving immaturely etc. Child like is always used to indicate that somebody is being naive or acting in an innocent manner. Good question because they are commonly misunderstood and used incorrectly as synonyms interchangeably.

Childish negative connotation whereas childlike is more innocent and postive

Childish usually mean silly or immature. While usually has more positive qualities of a child, like innocence or trusting.