Should we have different types of homicide?

The criminal justice system distinguishes between various types of homicide. Although all types of homicide involve one person killing another person, criminal law divides such killings into two categories, murder and manslaughter, with murder involving "malice aforethought"—that is, a deliberate plan in advance of the act of killing someone.
There are strong arguments for making some distinctions among types of homicide. The most obvious is the distinction between deliberate and accidental homicide. For example, if someone is driving on an icy road under the speed limit, skids on a patch of black ice, and accidentally hits a pedestrian on the sidewalk, someone has indeed died, but the driver had no intention of killing the person and is probably utterly horrified by the course of events. In fact, the act may not be considered a crime.
The next type of involuntary manslaughter is more problematic. Imagine that a driver was under the influence of drugs or alcohol, or was driving substantially over the speed limit, and accidentally hit a pedestrian. In such a case, there is an element of negligence, but the perpetrator may be struggling with substance abuse issues or simply young, thoughtless, and impulsive. While the act is definitely criminal, there is a major difference between this and someone, for example, who deliberately kills during the course of an armed robbery or a rape. One major difference is the possibility of the person being rehabilitated through substance abuse and metal health treatment. That being said, the high recidivism rates for impaired drivers suggest that strong sanctions may be needed.
Obviously, there are a wide range of possible scenarios in which homicide may occur. Society's response to such homicides should be based on evidence concerning the possibility of rehabilitation. A serial killer or gang member who has deliberately killed many people and perhaps committed other criminal acts is unlikely to change and needs to be incarcerated for the protection of society. Someone with a substance abuse or mental health problem who commits involuntary manslaughter may be a person who can be rehabilitated and become a productive member of society with appropriate monitoring and support mechanisms. Therefore it makes sense to treat these types of crimes differently.