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I suspect that the reason we have stronger prohibitions against genocide than against random mass murder of equivalent size is not that genocide is worse, but that it is more common.
It's easier to form, motivate, and communicate the idea "Kill all the Foos!" (where there are, say, a million identifiable Foos in the country) than it is to form and communicate "Kill a million arbitrary people."
I suspect that's not actually true. The communist governments killed a lot of people in a (mostly) non-genocidal manner.
The reason we have stronger prohibitions against genocide is the same reason we have stronger prohibitions against the swastika than against the hammer and sickle. Namely, the Nazis were defeated and no longer able to defend their actions in debates while the communists had a lot of time to produce propaganda.