It is primarily a matter of register: "slay" is more formal, more old-fashioned than "kill". It is also narrower in meaning. "To slay" implies that the death was intended, was probably violent, and that a weapon was usually used. It also implies hostility - you might slay your enemy, but the verb would not be used for accidentally killing a friend.

There is no difference in the meaning. They are synonyms... two words that share the same meaning. In English literature, 'slay' is often used more in terms of combat, even though it has the same meaning as 'kill'.

Slay is usually more violent. You can kill a person or an animal by lethal injection, for example, but you wouldn't call that slaying them. Stabbing, shooting, or any other violent means could be slaying.

You slay someone in battle. You kill someone any old how.