I have a vague idea of the three words kill, murder and slay, but I am not sure exactly what makes the verbs different (as well as the nouns killer, murderer and slayer). When do we use each of them?
One can kill any living being, whereas murder is reserved for the killing of human beings. Murder usually implies malicious intention, whereas killing can be accidental or spontaneous. Slay implies killing with violence. It is often used with dragons: to slay a dragon.
Kill - the ending of a life.
Slay - the deliberate ending of a life by another party.
Murder - the unlawful ending of a human life by another party.
Commit suicide - the deliberate killing of oneself.
Execute - the legal (or sanctioned by some authority) killing of another person.
There are many other words to describe killing.
The idea of "kill" vs. "slay" which has been offered here [above] as distinctly opposite of their correct use, (indicating the poor direction our education system has taken in the last 100 years.)
The word "kill" is the word that carries the connotation of malice and "wrongfulness" whereas "slay" is a simple statement of fact. Slay is the one-word term for causing death.
While they are often used in place of one another there are many examples that form and explain [by example] the differences. One distinct example is the 6th of the Ten Commandments, (Thou Shalt Not Kill,) wherein there is very clearly the connotation of a wrongful act.
Those who choose to take the very broad view that this Commandment applies to all forms of life-taking are playing the game of semantics. In the writing/composition of the King James Version of the Holy Bible, it took scholars approximately 30 years to debate these subtle but distinct differences, the ultimate choice being the one that has lasted the test of time.
Kill (normally) means "murder".
Slay (normally) is the simplest way to say, "caused to die."