Homicide just means killing a human. If a police officer shoots and kills a rampaging criminal, or an executioner in a prison puts a death penalty convict to death, it is a homicide but not a crime; its considered a lawful or justified homicide.
Manslaughter and murder are both types of criminal homicide. Murder is when the killer intended to kill. Manslaughter means the killer didn’t necessarily mean to kill the victim, but should have known that whatever they did (like drunk driving, or shooting a gun in the air) was likely to kill someone.
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