What is the difference between ПОЧЕМУ and ЗАЧЕМ?

A dear friend and student of mine, Gale suggested this as one of many topics for the blog answering a question many students face: What is the actual difference between the words ПОЧЕМУ and ЗАЧЕМ?

The first interrogative word ПОЧЕМУ = why and can have a couple different meanings with first one being just "why" as in "what is the reason".
E.g.: Почему ты не читаешь? = Why aren't you reading?
Не понимаю, почему он еще не здесь. = I don't understand why he is not here yet.

The second meaning of ПОЧЕМУ is an equivalent to WHY NOT, an objection used as an affirmative answer to questions starting with "don't you" or "haven't you".
E.g.: Ты не сделал домашнее задание? = Haven't you done your home work?
Почему, сделал. = Why not, I have. / Why not, I have done it.

The second interrogative word ЗАЧЕМ = why as in "what's the purpose" or "what for". It is used when the idea of the question is "With what purpose?" or "What is the goal?"
E.g.: Зачем ты готовишь ужин? Мы ужинаем сегодня в ресторане. - Why / what for are you cooking dinner? We are having dinner at a restaurant today.