Looking around a crowd, and setting a shrapnel bomb on the sidewalk next to children...that's murder
It is but ONE form of murder, ONE of MANY.
Executing a death sentence as punishment for that cold, calculated act of deliberate cruelty and murder isn't murder.
Yet, if his parents had executed him when he got home, for precisely the same reason: "as punishment for that cold, calculated act [...]" it would be murder again, right? So... apparently that "reasoning" isn't what makes it "not murder". What makes it "murder" is the trappings of legality and due process... its purely semantics.
murder is premeditated homicide that the state has declared illegal
execution is a specific premeditated homicide that the state has declared legal
Make no mistake the ONLY difference between them is the writing on paper that makes one legal and the other not. The writing is the difference. In some cases it is a sufficient difference to justify it being different.
If we execute an innocent person... though... is there any difference at all?
After he's captured, in handcuffs, in prison, and under guard... Any threat he poses is well and truly neutralized. So, no, killing him at that point is NOT self defense.