According to the dictionary:

Kill: to deprive of life; cause the death of
Murder: the crime of unlawfully killing a person especially with malice aforethought

Without going into a scholarly examination of these definitions the one striking difference is the word "crime".

Life is a privilege given by G-d -- but with conditions. Here's the first condition: if you don't value the life of others, you lost your privilege.

If you take a moment to think about this you realize that the murderer and executioner kill for two very opposite reasons and since they are opposites one can be evil and one can be good: the murderer murders because he doesn't value life. The executioner kills because he values life, and as such must remove any threat to life.

Many ask who is to determine when someone loses the privilege to live. There are many answers to that; here are three:

Life is a privilege given by G-d -- but with conditions. Here's the first condition: if you don't value the life of others, you lost your privilege

2) A society will decide what acts are threatening to the society at large and must therefore be stopped even at the cost of killing the perpetrator of these acts.¹

3) Most importantly in our context, the Jewish context, G-d determines who should live and who should die, and He told us in the Torah that we may NOT murder, but at times we MUST kill.

(Parenthetically, G-d knew that we Jews would use the logic that "all killing is evil" and therefore would have a problem killing murderers -- and He therefore forewarned this thought. When commanding us to execute a murderer, the Torah tells us:²   "And you shall not pity him, but you shall abolish [the shedding of] the blood of the innocent from Israel." Rashi explains: "And you shall not pity him:" I.e., you should not say, "The first [person] has already been killed; why should we kill this one too and cause two Israelites to be killed?")

The same reasoning regarding an individual can, and should, be applied when discussing nations at war.

A nation that carries out preemptive attacks against a neighbor who poses no threat and wishes no harm to the attacking country is a nation that is committing murder.

A nation who defends itself against such an attack from such a neighbor is justifiably and rightfully fulfilling its duty of killing people who don't deserve to live, thus protecting those who do. According to the Torah we have an obligation to kill anyone who desires to kill us!³

Incidentally, a nation who is being attacked constantly but for the sake of good PR does not take all necessary measures to defend its citizens is now an accomplice to the murder committed by its murderous neighbor. The death of innocent civilians in this case is indeed tragic.