"Execution" is what we dispassionately do to criminals who don't deserve to share the planet with the rest of humanity anymore. "Execution" involves justice and punishment for past wrongs.
"Killing" can mean any number of things.
Osama bin Laden was not worthy of living among decent human beings. He was executed as a result.
Myt first reaction was “Really? How do you know? You obviously weren’t there. Shut up.”