What is the difference between deontological ethics and teleological ethics?

Imagine that a man with an axe breaks into my home, where 5 of my family members are.
Deontological ethics is duty based (this is easy to remember because of the D for deontological and duty). They would say: "I have a duty never to kill, no matter the circumstance." For the deontologists, even if a man with an axe ran into my home ready to kill my family, it would still be wrong to kill him, because it is always wrong to kill, even if it saves lives.
The Teleological ethicist on the other hand sees that consequence is the most important thing. They focus on the outcome, not the duty. For example: "If I kill the man with the axe, then 5 of my family will survive, and only one person will die. If I don't kill him, 5 will die and only one will live. Therefore, it is right to kill him/"