The relationship between belief and knowledge is impossible. Believers in a claim typically say that they know that claim. For instance, those who believe that the Sun is a god will report that they know that the Sun is a god. However, the terms belief and knowledge are used differently by philosophers.
Epistemology is the philosophical study of knowledge and belief. A primary problem for epistemology is exactly what is needed in order for us to have knowledge. In a notion derived from Plato's dialogue Theaetetus, philosophy has traditionally defined knowledge as justified true belief. The relationship between belief and knowledge is that a belief is knowledge if the belief is true, and if the believer has a justification (reasonable and necessarily plausible assertions/evidence/guidance) for believing it is true.