Kai-Petri has it!

There were two triggering designs. Little Boy used conventional artillery technology to fire one subcritical U-235 mass into the other. Fat Man used a relatively unknown implosion technology, symmetrical shockwaves directed inward to compress a subcritical plutonium mass (hence its almost spherical shape).

Field tests of the prototypes (less fissionable material) in drops from a B-29 established confidence in the Little Boy approach. Trinity was deemed necessary to establish confidence in the Fat Man approach.

For those interested in more history in this vein, see http://www.ntshf.org/index.htm (Nevada Test Site Historical Foundation). They dedicated their Atomic Testing Museum in Las Vegas this past week.