A common misconception exists about people who want to die.
Some people want to kill themselves. They not only want to end their existence, but they want to do it themselves; they are the self-loathers. This is akin to hating an enemy so much you would like to murder them, such as a backstabbing friend or a cheating spouse (and probably the dumb broad he cheated with.) In this instance, the suicidal subject is their own enemy and therefore there exists an inner desire to annihilate the enemy. Self-Murdering types tend to self-injure among having other unhealthy habits. These people do indeed want to die, but they don't just want to die, they want to murder their own being.
Other people simply want to die. They no longer wish to exist. This could be for a vast amount of reasons; loss of faith, loss of stability, long-term depression, hopelessness. This is a less enthusiastic kind of suicidality. You may find these people sleeping a lot - taking cold pills to knock out, drinking until they pass out, hitting themselves in the head with a baseball bat. They may feel like sleeping is the next best thing to death, save the nightmares they have incessantly. These types may self-injure, like the first type, and not necessarily out of self-loathing, but due to the psychological release and perhaps being able to reconnect with reality momentarily.
The solution for both of these types is self-offing. For the first type, it's the goal; to murder the self, the enemy. The the second type commits suicide as a byproduct of no longer wanting to be. Both types are suicidal, but the nature of their suicidality is vastly different and even more vastly misunderstood.