We tend to see the bombing of Hiroshima and Nagasaki now through the lens of the thermonuclear age where superpowers had vast arsenals of thermonuclear tipped weapons ready to fly at a few minutes notice. As the first and only nuclear weapons used we assume that these must somehow be set-apart and treated as special, a lot of people also assume that they were specifically authorised by Truman (as the use of nuclear weapons was a strictly controlled presidential prerogative during the nuclear age).

Another way of looking at it is not as the first nuclear bombing but as the last bombing of the second world war. In that context, even the deadlier of the two, Hiroshima, doesn't seem any worse than the strategic bombing in the rest of the war. Not just Tokyo and other Japanese cities, but the bombing raids on Germany, the Blitz in the UK, not to mention the vast horrors inflicted on civilians in Eastern Europe and in China. This context also explains why the last explicit order to use the bombs was weeks before they were dropped and came from General Groves, while there was some high level discussion about targets, the prosecution of the war was a purely military matter.

Of course in retrospect, people began to see nuclear weapons as uniquely horrible, but that's really only because they became so powerful and so numerous.