The idea of the atomic bomb was built upon scientific discoveries that were published in the open literature and available to all nations. Nuclear fission and the fission chain reaction opened up the possibility of making a weapon to scientists in the US, Germany, France, Italy, UK, Denmark, Soviet Union, and even Japan. The fact that these were discovered just on the eve of World War II (late 1938/early 1939) created a context in which many of the scientists in these countries went to their governments and said, "hey, there's this possibility out there of a new kind of weapon — maybe we should study this a bit?"

This lead to small research programs in multiple countries: the UK, the US, Germany, the USSR, and Japan. Of these research programs, one of them (the UK) concluded that the bomb would not be that hard to make at all, and worried that Germany would be trying to make one. They lobbied the US to build it, and the US ran with the idea. Only the US moved from the research/pilot plant stage into a production stage, and that led to the building of the actual bombs. The US did believe the Germans were working on an atomic bomb for awhile, and this motivated them to go into an "all out" effort, but by November 1944 they understood the Germans had not made substantial progress. By this time most of the American efforts on the bomb had shifted to consider Japan to be the target.

In Germany, the research program concluded that building a bomb was probably not within the scope of any country during the war (it was going to be very hard and expensive), and so Germany did not need to prioritize it. Instead they had a reactor research pilot program that worked to get a pilot-scale reactor working, almost accomplishing that by the final days of the war. But this was not a bomb program and them getting the reactor working would have had no impact on the direction of the war (especially at that point).

So to answer your question (which is not silly): the reason they were both working on these issues during the war is because they were inspired by exactly the same discovery. But the Germans ended up getting nowhere close to the Americans by the end of the war. The idea that there was a real "race for the bomb" is often hyped up both for dramatic tension, and to make Americans feel better about having made and use the bomb.

One can read about these events in many sources; Rhodes' The Making of the Atomic Bomb is still the standard reference.