What is the difference between think and believe?

In both ''think'' and ''believe'' there is a verb of cognition (awareness, certainty). The difference lies in the nature of truth value predicated of the complement clause by the matrix verb( believe vs. think)

We could couch this truth value predicated either in terms of a) epistemic modality or b) evidentiality. Either way, the verb ''think'' denotes less confidence in the truth of the complement clause than the verb ''believe''(but they both denotes lesser confidence than the verb ''know'')