The short answer: At the beginning of the Manhattan Project, enough of the science of fission was uncertain, and General Leslie Groves was given so much power, that he decided to try to build a bomb any way they possibly could. There were two possible materials to use, uranium (U) and plutonium (Pu), and they went after both materials.
The longer answer: The Manhattan Project started with a basic design, known as the Little Boy, or gun-type weapon. They didn’t know if they would have enough either U or Pu nuclear fuel for a weapon, so they chose to pursue both types of fuel. Also, while they knew quite a lot about uranium, plutonium was a relative stranger. (The Pu gun weapon was nick-named “Thin Man.”)
Uranium is a natural element that is mined (At the time much of ours came from Africa, but the Germans had set off alarms in the US scientific community when they invaded what was then Czechoslovakia, where there was another known supply.) and occurs as mostly a slightly heavier isotope, U238, and a small amount of slightly lighter, but fissionable, U235.* The two isotopes need to be separated to increase the proportion of U235. This is very difficult because the two isotopes are the same element and behave the same chemically. The only handle they had for sorting them is the fact that U238 atoms are about 1% heavier than U235 atoms. That means they move ever so slightly more slowly through filters, or when spun, they drift ever so slightly more to the outside. The Manhattan Project scientists tried a number of ways to enrich their uranium and ended up using a combination of techniques, but it was difficult, expensive, and slow.
Plutonium does not occur in nature in any considerable amount. It is made in special nuclear reactors by bombarding other elements with neutrons. While the reactors were huge and expensive, separating the Pu is comparatively simpler, because it is chemically different from the other by-products.
The bad news came half way into the Project, when chemists studying Pu discovered that it was too reactive to use in the gun-type bomb design. This had been a possibility all along, so early research had explored the idea of the implosion, or Fat Man type of weapon. By this time Pu production was strong enough that they decided not to drop the Pu program, but to take it in the new direction. The U235 supply was by then good enough that they decided to keep going with that design as well. In the end, they created two types of weapon. They were confident enough in the U gun weapon that they didn’t test it before dropping it on Hiroshima. The uncertainties about the Pu implosion weapon led them to make the Trinity device test at White Sands before they dropped Fat Man on Nagasaki.
*Little physics lesson: An element is determined by the number of protons (atomic number) in its atoms’ nuclei. An isotope of an element has the same number of protons, but can have different numbers of neutrons. The atomic weight (the 235 or 238 after the U) is the sum of neutrons and protons. A neutron or proton has a value of 1.
