There are other, simpler circumstances where you can show guilt to a reasonable degree, such as self-defense. If someone is shooting at you you can shoot back, for example. No murder.
Of course trials at that time and place were anything but fair, but we don't generally refer to those state-run executions as lynchings (perhaps we should).
And how is any of that not torture? Seems like your definition of torture is just "doesn't result in death."
Anyway torture, simply defined, is an act causing extreme pain in someone. And not just for five seconds. Hanging-done-wrong can be torture. Many ways of killing someone are torture. But the fast methods are not. Tell me your definition if it can somehow apply to the use of a guillotine.
Well, the real definition distinction is that when it is legal it isn't murder, and I think that that distinction is more than just semantic, as I think it ties into some substantive differences in the social forces at work.
That's not to say that there aren't also areas of substantive similarity between that form of ritualized killing and others including ritualized murder.