Kill vs. Execute issue mainly comes from peoples understanding of the Old Testament.
“Thou shall not kill” confuses many.
In the original language (Hebrew) this was meant murder not kill.
It was murder that God was condemning.
Now when you apply this to hunting, wartime killing, executions. The term kill make more sense.
It is killing, just not murder.
Well it means “Thou shalt do no murder” - murder is malice aforethought meaning a planned killing of one human by another. God gave us laws and justice for us to carry it out legally in due process; some guy, like this one, went into a home and beat a woman senseless then strangled her. That was murder. His execution was not.