They were certain the U235 gun type would work and did not feel it was necessary to test it. The plutonium (the round bomb) was the implosion type. They were not sure it would work (if the explosives do not explode perfectly it does not go off) so they tested one. It was not a "plutonium gun-type bomb".

IIRC the test and the two war bombs used up all the refined material on hand. Of course Japan did not know it, but it was several weeks or months later before more cores were ready. For a short time after Nagasaki, the world was a nuclear bomb free zone.