Murder defines an actual illegal act. (Defined by law) Homicide defines the act of killing another human being, not necessarily illegal. (for example in a war) While murdering someone is an act of homicide, an act of homicide isn't necessarily murder.

Homicide is a broader term than murder. Homicide means any killing of one person by another, including things like self-defense and negligent (rather than intentional) killing. Murder means the intentional, unjustified killing of another person.