Law at biblical times had a different foundation than today. Today the foundation is legal positivism, which is the philosophical decoupling of moral and law (which sounds terrible at first glance, but is important if you think it through). Therefore, it is not useful to apply the definition of the terms from back then, because the whole context in which they were used doesn't exist anymore.

In the Western world, the meaning of murder and killing is different and while that described action might be an unlawful killing (by accident) it most likely was not a murder.