In general the take was that human created nuclear weapons were infeasible (regardless of design) because of what was thought to be the barrier to cross to achieve a chain reaction.

The Frisch–Peierls memorandum changed that understanding ... provided that reading of the FP-memorandum was convincingly conveyed to people that made things happen, what Einstein put to paper (and was ignored) and that Oliphant pushed through in person.

Little Boy on Hiroshima was a gun design, a grossly inefficient McGyver that used some 64 kilograms of enriched uranium to successfully convert less than half a gram to energy.

Fat Man on Nagasaki was an implosion device - a necessary design change due to simply not having enough uranium or an enrichment pipeline to sustain the needs of a gun design.

The first device detonated, at Trinity in the USofA, was an implosion device, created to test the more difficult design.

Further, there was an abandoned / discarded "Thin Man" device IIRC.

These were all alternative implementations that were pursued after the FP-memorandum was pushed about to make the case that weapons were apparently possible rather than not yet achievable - the prevailing belief in the US prior to Oliphant doing the rounds.

  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.