Homicide: literally, the killing of a person by another.
Murder: the unlawful and intentional, killing of a person by another, or unintentionally causing the death of a person while in the commission of a dangerous felony.
The word "homicide" does not describe whether the act was justified or not, or intentional or not, only that the death of one person was the result of the actions of another person. Therefore, a homicide investigation does not necessarily equate to a murder investigation (although it may evolve into such), particularly when the death may have been accidental, or with a justification such as self-defense.