Luiz, one can kill an animal, a human, a flower, or something else, but one can only murder a human being. Slaying someone is killing them in a very violent way. She killed the squirrel on accident. He murdered the man acquitted of his crimes. The king ordered the entire village population to be slayed.

The word „slay“ is archaic and I’d never use it. You might read it, but it’s very old. Nobody is going to say it anymore. When it was used it was sort of the equivalent of „massacre“. Murder and kill have legally different meanings. Murder implies an intent to kill another human being. You might use it with regards to an animal, but that would be just for emphasis: „She murdered my cat!!“ Kill is just a general term that means to end someone‘s life. This can either be intentional or unintentional. The family was killled in the tragic car crash (which was accidentally caused by the icing on the road or something). But, „the guy who broke into the house murdered the family before robbing them.“ So, just think: murder=intent to kill Kill: either intent to take a life of someone or accidentally taking the life of someone. Slay: forget it. Out of date. But, understand the word if you read it.