How much worse than a standard firebombing were the nuclear weapons? Is there validity to the idea that the Japanese government didn't even recognise that Hiroshima and Nagasaki had been hit by a nuclear weapon instead of several incendiary bombs? What would have been the projected death count if major cities like Tokyo and Kyoto were nuked instead of the large but comparatively smaller Hiroshima and Nagasaki?
Funnily enough, I wrote about this very topic a few years ago at some length here: Tokyo vs. Hiroshima. The very brief answer is that even the firebombing of Tokyo was far less deadly as a percentage of population or area destroyed than Hiroshima (Tokyo was many times more populous than Hiroshima, so even a lower mortality resulted in high casualties), and that most firebombings after Tokyo were far less deadly (because the Japanese understood what the tactic was and would work to take better cover when they saw hundreds of B-29s approaching). And I do make some guesses at the projected death count for dropping a Hiroshima-style bomb on Tokyo — it would likely have been 2-4X more deadly than the firebombings.
I haven't tried to run the calculation on Kyoto. I'm not sure I have the population density information I would need to do the calculation, but I guess I could look into it at some point (not today, though).
In terms of the Japanese response: they understood fairly quickly that something awful had happened at Hiroshima, and assumed it was some kind of firebombing raid. However their understanding of this was changed by US announcement of the use of an atomic bomb against the city. They then sent a scientist to Hiroshima to determine whether it was indeed an atomic bomb (they didn't take the US's word for it, understandably). He confirmed, on the evening of August 8th, that what he saw was consistent with an atomic bomb (the radioactivity and point-source nature of the blast damage is very clear evidence of that). The next morning the Japanese high command met to talk about the Soviet invasion of Manchuria (which happened on the evening of August 8th) and while they were in that meeting, they got the news of the attack on Nagasaki. They do not seem to have doubted their scientist nor that the second atomic bomb claim was a real one.