Trinity and Fat Man were plutonium bombs, they needed to be implosion designs because it was realized that a gun wouldn't work using plutonium [1].
These weapons were, however, as different as their monikers imply. Little Boy was a uranium, gun-type weapon, whereas Fat Man was a plutonium, implosion-style weapon. Two types were needed because there was only enough uranium for one gun-type weapon, and the U.S. government knew it would need to make more than one weapon.