I think it is difficult to call kill a synonym for murder. Those have two entirely different connotations with incredibly different theological implications. Saying not to Kill implies a complete ban on the action. It practically makes immoral anything but pure pacifism [which completely makes zero sense in the context of the book it is written in].

Murder however, is a very specific type of killing done with very specific moral implications. Murder is a small subset of "kill" implying an unjust action or however you want to word it. While the original Hebrew had a bit more richness in potential meanings than our word murder, it is still clearly talking about murder and not the general action of killing which would be a different word used. That is speaking in english of murder vs kill, and it turns out that there is a similar distinction in both Hebrew, and Greek [Greek is very important for the old testament as well given the incredible importance of the Septuagint to the New Testament writers and the early church. Not saying it is a perfect translation though either or anything so grand of a declaration. Just that it is one of the most important old testament documents]

I am doing this from memory so I may not have this next part "perfect" but I believe it is the word used could mean murder, or accidentally killing someone in Hebrew [while there is a more generic word for the action] depending on the context. Clearly a command not to murder makes more sense than a command not to do something accidentally [if it was accidental, you were trying to obey the command anyway!] and even if it were meaning just accidental or maybe both, it wouldn't include ALL actions of killing by that word. At best it could mean murder + accidental deaths [which the second being kinda awkward as a command, but still reasonable to say those are bad too when you mean the first].

Maybe the word bad translation would be better than mistranslation, but at least to our modern english, it is simply a bad translation of the term.

Not to mention, the entire context of a general kill makes ZERO sense in the context of the Pentateuch. Context is important and king. Occam s razor makes quickly obvious by the context what it means. Dont' create yourself magical contradictions when the obvious answer is SO simple and obvious. Those who are trying to argue otherwise are often just KJonlyists which I am not even going to get into that nonsense here or people really stretching and trying to ignore a massive pile of evidence that all leads one way and isn't even that controversial for most scholars.

Not saying it can't be argued with, please forgive me if it sounds like that. I am just saying the evidence is very weak from the testimony of the early hebrew to other languages translation, all we know about hebrew, inference to the best explanation, and context in the book and passages it is written in [for the context one if often helps to not assume an author is so dense they are going to contradict themselves on a massive scale just a few words later. Maybe they did, but give them the benefit of the doubt and check if maybe there is [and is often a more obvious] an answer].