Suppose, for example, that a child has not yet realised that X knows that P implies P, and so uses know interchangeably with believe. We would say that he had not yet mastered the concept. On the other hand, if he has grasped this logical pint but is unable to think of a single instance of something he is prepared to call knowledge, we would regard this as a failure of memory or experience (or a mark of philosophical potential) rather than of understanding.
Cheekiness aside, it actually takes children a while to fully understand the difference between know and believe. According to Bartsch & Wellman‘s classic corpus study, Children Talk about the Mind, children begin understanding those two verbs in their third year of life, but they don’t appear to have truly mastered the concepts until around the age of 4. This is in contrast with verbs of desire like want, which kids know by the time they are 2.
Why are kids slow to understand know and believe? Some of the difficulty appears to be in understanding false beliefs — that is, the fact that the contents of a person’s mind may conflict with the actual state of the world (John believes Algeria is in South America, but it’s not). Until a child has mastered that concept, there isn’t any substantive difference between know and believe.