If you're looking at Old Testament law (thou shalt not kill) then there is clearly a difference between executions and murder. There were multiple words for "kill," each with a different meaning. The commandments use the verb for "murder an innocent," not the verb for killing in war, execution, self defense, or killing an animal.
I certainly agree with you. The 2 generations of "Hapiru's" that traveled with Moses certainly understood how the commandment regarding "kill" was to be interpreted.... far better than the Vatican does today! Those who corrupted the camps with abominable practises or who murdered in cold blood were executed and Israel's enemies were slain in war often by the direct power of God! The transcriber of the Mosaic code was an advocate of capital punishment!
Ultimately God's son died the death we all deserved for our transgressions of the law!
So you want to interpret the 10 commandments? Look how the ancient Israelites did so from their practices!