Homicide is essentially the murder of a human by another human. It is done indiscriminately in many different video games, and is, in fact, the pure and only objective in certain games.
It is essentially killing things that are not human. This takes place in video games when you kill robots, aliens, or anything else that is obviously not a human being. This includes sentient AI, plants, and animals as well.
Many games suffer from a paradox existing within their main characters. Generally, these people are viewed as heroes or tortured souls, who take huge amount of deliberation on ending the lives of people, when their character is exposed in cutscenes or in-game movies. However, in order to complete their objectives, they must generally kill hundreds of criminals, cops, soldiers, or just general people to get from point A to B.
Assassination is a special type of murder in which a person kills another one and plans it out for political, ideological, or financial reasons.