Several points to be made.
1) The use of atomic weapons in WWII was moral and ethical and probably saved more lives/suffering than it consumed by an order of magnitude.
2) In order to understand the distinctions between murder and killing, one needs to understand legitimate authority and the justification in the use of deadly force.
3) WWII and the Pacific War especially are probably the best documented of all wars, in part because it was total war.
In total warfare, all elements of society are engaged in warfare with the opponent nation. Historically, there hasn’t been a war where there were more military casualties than civilian casualties. That’s why people form armies, navies, the military, and rally behind leaders. They are safer in well organized numbers than as disorganized mobs of individuals. Those who refused and preferred to fight an army on their own, as individuals, are generally never heard of again, except by those who bury their remains.
In total warfare, the war also tends to be a war of attrition. Operationally, destroying resources of an opponent implies the enemy has less resources to attack friendlies. This means we are using deadly force to influence the will and ability of an enemy from opposing our volition. We act within legitimate authority to impose our volition legitimately upon the enemy.
When Japan attacked the US at Pearl Harbor, she had not issued an ultimatum nor other negotiation by which any sane or rational person or government could comply with her volition. She engaged in a surprise attack with full knowledge and intent of destroying other nations in blatant disregard for human life or legitimate authority over those people.
At Hiroshima and at Nagasaki, both instances were in states of Total War between combatants and both cities had operational and strategic import for their placement on target lists in a campaign to ultimately cause the defeat and unconditional surrender of Japan to the US and Allied powers.
The atomic bombs developed were not specifically designed to be indiscriminate weapons. Nobody gave criterion to mad scientists to build something that would not discriminate in who might be injured by them. They were designed to cause as much blast and destruction as possible for a given payload. Their scarcity also implied their extreme value in operational deployment, but as revolutions in military warfare, they also contained valuable psychological import.
Even in Vietnam, until computer based bombadier sights were developed circa the mid 1980s, delivery of airborne ordnance to pinpoint targets was not very accurate. If somebody needed a bridge taken down, like those in Vietnam, numerous sorties were flown with unsuccessful results.
The atomic weapons being developed and deployed in Japan made it clear and obvious to senior decision makers that resolute willpower would still be inadequate to resist American invasion of the Japanese homeland.
"1) Atomic weapons …probably saved more lives/suffering than it consumed."
I take it then that you are a consequentialist: that you hold that no act is wrong in itself, but any act can be justified on the basis of its consequences.
(Is this your belief? If not, tell me what and why.)
If so, I would be interested in what sort of consequences count for you: is it a calculation of the number of human lives saved or ended, and that's all? Can this calculation have any cut-off point in time, or does it extend indefinitely?
Or do you, like the utilitarians, gauge "good" and "evil" by the increase or decrease of pleasure and pain? The promotion of an advanced civilization, and the suppression of a barbarous one? Or is it the kind of consequentialism that computes the number of people whose preference is satisfied by that action? Do moral and cultural consequences count, the suppression of depravity (e.g. Canaanites and their child sacrifices to Moloch, marriage by bride-capture, entertainment by pederasty) or the promotion of elevated values (the Reformation, Democracy, a Catholic realm for the Catholic monarchs, the Greater East Asia Co-Prosperity Sphere, the Workers’ Paradise?)
These aren't idle points, as I think that ordinary bad men usually only do a very moderate number of homicides and are satisfied with that. They're not consequentialists. But to rack up a truly large number of noncombatants killed, you generally have to be a "good" man or men: a government, or a religious movement, or a very, very high idealist, with a complete sense of justification that the good consequences outweighed regrettable but realistic expedients like "killing the innocent."
2) In order to understand the distinctions between murder and killing, one needs to understand legitimate authority and the justification in the use of deadly force."
Legitimate authority is one of the criteria which must be satisfied in the decision of entering into war, but it’s not the only one. The bombing of Pearl Harbor was clearly an act of aggression and justified the US House of Representatives making a declaration of war. Yet satisfying those two criteria for jus ad bellum (just cause and just authority at the outset) doesn’t mean that subsequently anything and everything is justified (jus in bello). What was justified at that point, was physically destroying Japan’s military forces.
(I think you have noticed that I am not arguing for pacifism here. Good. I am convinced that pacifism is a false doctrine, and also an extraordinarily harmful one: unusually harmful for a thing that sounds so noble.)
3) WWII … was total war…all elements of society are engaged.
I dispute that. Even if a regime is whipping up the total populace to make total war, it is in fact not so. In actual fact, many or even most people are still doing things which are unaggressive and morally blameless: the farmer farms, the mother mothers, the just man (as Hopkins says) justices: makes a distinction between good and evil.
It might be argued that sometimes it's devilishly hard to figure who and what is a military asset. Of course: every time you draw a line, there are some things that are borderline cases, and some things that are far to one side, or far to the other. But that is not an excuse for drawing no line at all. Normally, people act normally. (There's a good maxim.) And so normally, the wood-hauler is hauling wood,which he must do be there peace or war. If there are IED's hidden in the woodpile, all bets are off: blow 'em sky high. But to kill everyone in the countryside, or everyone in the city, by intent: that's murder.
Or if not, what is murder?