The Difference Between A Non-Believer And An Unbeliever

He is known for being strong willed, stubborn, and doubting.  His name:  Thomas, one of the twelve disciples who walked with Jesus.  Mentioned a dozen different places in the New Testament, Thomas is usually thought of as a "show me" sort of person, short on faith and long on doubt.  But, is this characterization really accurate?  Or was Thomas a perpetual pessimist, the kind of person who describes the partially filled glass of water as "half empty" instead of "half full?"