Fat Man and Little Boy
<Fat Man and Little Boy used more than different triggers, they were entirely different designs. Little Boy used enriched Uranium 235. It used a cannon to force two subcritical masses into a single supercritical mass. The design was so simple (but quite inefficient) that they didn't bother to test it before dropping it on Hiroshima. Fat Man used Plutonium and the implosion technique. That was the design tested at the Trinity site in New Mexico and dropped on Nagasaki.