A homicide investigator collects clues and information regarding a homicide. They rundown leads and followup with evidence and suspects. A lot of paperwork is involved and it's not nearly a glamorous as on TV.
A homicide investigator researches the death of a person. They determine whether it was accidental, suicide, or murder related. The investigator is thought of as a detective in the police force.
A homicide investigator works closely with the police force and anyone else involved in the case. They may be interviewing suspects and working with a forensic team discussing evidence. The ultimate goal is to help solve the crime.