I've heard this contrasted as 'knowledge', where you intellectually assent to something and can make predictions from it and 'belief', where you order your life according to that knowledge, but this distinction is certainly not made in normal speech.

A common illustration of this distinction (often told by preachers) is that Blondin the tightrope walker asked the crowd if they believed he could safely carry someone across the Niagra falls on a tightrope, and almost the whole crowd shouted 'yes'. Then he asked for a volunteer to become the first man ever so carried, at which point the crowd shut up. In the end the only person he could find to accept was his manager.