Not every kind of killing is a murder. Only an intentional killing is a murder. And not every intentional killing is a murder--just killing in a just war isn't murder. Only a wrongful intentional killing is a murder.
But not every kind of wrongful intentional killing is a murder. Jim takes a vow of non-violence, is drafted into the military notwithstanding the vow and intentionally kills in a just war in a way that is wrong due to violation of the vow (in some cases it might be that the needs of defending the innocent could override the vow, but stipulate that this isn't one of those cases). This intentional killing is a vow-breaking rather than a murder. Samantha is a police officer who shoots down a terrorist shooter who is on a rampage. However (and Samantha knew this), this terrorist is a crazy scientist who has just discovered a cure for a medical condition that kills millions, a cure that he was going to share after murdering ten people. Killing the scientist is wrong, but it's not a murder. Frederick is an executioner executing a duly convicted person who clearly deserves death, but this is a case the death penalty is impermissible for reasons other than justice (say, because there is a less violent way to protect society, which according to Evangelium Vitae implies that the death penalty is wrong). Martha intentionally kills an unjust aggressor in a war where her side meets some but not all the conditions of a just war: there is just cause, but the condition of reasonable expectation of success is not met.
In the above cases, the intentional killing is wrong but for reasons other than justice to the person killed. Indeed, in at least the cases of Jim and Samantha, the person being killed isn't being wronged at all.
I hypothesize that an intentional killing is a murder only if it is wrong as an injustice to the person killed. But this condition is still not sufficient. Suppose Jim instead of taking a vow of non-violence promised Patricia that he would never do anything to physically harm her, unless it was his moral duty to do so. And now Jim faces Patricia in a just war, under circumstances such that apart from the promise it would be permissible but not obligatory for him to kill her, and with the promise it is impermissible for him to kill her. Killing Patricia would be unjust to her, but the injustice is that of breaking a promise to her, rather than that of murder.
It's looking to me that murder is an intentional killing that is wrong due to a particular kind of injustice to the person being killed. It is difficult to specify the particular kind of injustice in a non-circular way, though.
Corollary: If suicide is a form of murder, then it is possible to be unjust to oneself.