Used by many people interchangeably to some extent leads to believe that these similar terms.. but are they so?
Trust is when you believe someone... While Belief is what you trust to be true...
Our life is nothing but the game of these... Sometimes when your confidence is low, you like to trust & take decisions and while your confidence levels are high enough, you trust in yourself(which is nothing but set of beliefs) and try to carry responsibilities with you...
Belief is somewhat personal while Trust requires a other end.
Both when shattered bring you pain.. but when beliefs shatter, you have a chance to have other beliefs. Whereas when trust is shattered, it takes a while when you start trusting somebody else..