TO KILL is to cause someone or something to die. “Smoking can kill you.” “Your friends were killed in a plane crash.” “Food must be heated to a high temperature to kill harmful bacteria.” TO MURDER is to commit a crime of intentionally killing a person. “Her husband was murdered by gunmen as she watched.” “In the last year, terrorists have murdered several local journalists.” Or in the informal saying: “If she's late again, I'll murder her!”

Thanks for your correction, Norm!

Sophie -- You shouldn't pick the winner so quickly! Joao's answer was not 100% correct, because hunters kill their prey intentionally, not by accident. And a woman who deliberately killed her abusive husband or boyfriend might be found guilty of manslaughter, rather than murder. So I think Alexandre actually had the more correct answer!

to kill is to just simply end a life, however it may be done. to murder is doing it in a much heavy way like morbid.

It's also very common to use the expression "I want to kill 'someone'" as a way to express extreme dislike, anger or annoyance. Example: "I wanted to kill my husband when I saw him with another woman"