Manslaughter is when you kill somebody on accident. Normally, people don't get punished for this but if they do the sentence tends be very light. When placed in fiction, the accident usually occurs at the beginning of the story. The story would most likely have some relative/friend of the deceased attempt to get revenge on the suspect of the manslaughter. This would make the story a horror or even tragic tale. It would be a horror because someone innocent is being targeted by another who is probably willing to kill anyone who gets in the way of their revenge. It would become a tragedy if the innocent person is killed. Ironically, if the innocent person does survive, they would likely have to kill the attacker in self-defense.
Normally the last resort of self-defense, it is not uncommon for someone to kill if the attacker threatens to cause serious harm. In fiction this is quite common in action or horror stories. If it is an action story then it would likely become an epic battle of survival. But if it is a horror story then it would likely be at the end where the last survivor enters a final showdown with the killer and kills their attacker, ending the movie.
This is the stereotype form of killers. Somebody who intentionally took away the life of someone else, usually an innocent victim. There are many reasons someone who attempt to murder someone in cold blood. It could be for revenge, maybe it is related to insanity (this also includes yandere), could have been the heat of the moment, maybe for wealth, a job, maybe even to protect somebody.
A cold blooded killing is when the killer feels no sorrow or regret specifically for the killing. This term most likely came from the idea that cold blooded animals were too primitive to have emotions.