Was the atomic bombing of Japan absolutely necessary to end WWII? Probably not. But for the US it was the most logical thing to do.
What caused the Japanese surrender was a combination of things.
It's untrue that the atombic bombing didn't have a different impact than regular bombings. When the Japanese flew over the bombed areas, they saw a huge area almost turned to dust. The psychological impact was much bigger. They thought about what 10 or 20 of those bombs could do.
On the other hand you had the Soviets indeed invading Manchuria, and possibly the north of the Japanese mainland. So Japan chose what they assumed was the better deal: surrendering to the US. They assumed that Stalin wouldn't go as easy on them as the Americans. Imagine Mr. psychopath, basically having control over your country.
The US had a few options:
They could have done nothing, and just let the SU invade Japan. A world where that whole region was in Soviet hands was obviously unacceptable for them.
They could have invaded Japan. That would have led to a lot of casualties, on both sides. Japan literally drafted the entire population by the end of WWII, so it would have been impossible for the US military to distinguish 'civilians' (who would surrender) from enemy combatants.
Not only that, but more importantly: the Soviets did invade Manchuria (after the bomb on Hiroshima was dropped). And they would have invaded the Japanese mainland as well, from the North. In that case you would have had the US and the SU fighting for influence in Japan, possibly a case like Korea.
Nuking Japan was the best option for the US: maximizing influence, minimizing casualties, on both sides (although the possible casualties on the Japanese side was probably not their biggest worry).
And for Japan, as a whole, it was probably the better outcome too (except for the people turned to ashes).
Was it morally right? Well, of course not, it's war. And that bridge was crossed a long time before they dropped those nukes. The hundreds of thousands of Japanese civilians that were burned to death in the strategic bombings could tell you that if they were still alive.