What's the difference...

Well, the bare basics:
A request would be a statement: "I request that you take out the trash."
A question would be a question: "Will you please take out the trash?"

Not to insult your intelligence, but the question has a question mark at the end. It's that simple. A request is a statement that solicits a favor, but is not phrased as a question. A request can be declined, but proper etiquette would require some kind of explanation as to why. And of course, just for clarity's sake, a demand simply gives an order without proper room for a decline.

Request: "Please take out the trash."
It's a statment, but leaves the person receiving the statement room to say decline, perhaps by saying "I'm sorry, I can't. I'm too busy writing."

Question: "Can you take out the trash?"
Simple. This can be declined with a variation of either "yes" or "no."

Demand: "Take out the trash."
This statement implies that there is no room for bowing out. You do it, plain and simple.

Hope that helps.

I"m going to differ with engmajor.

A request can be formulated as a question: Could you get the milk, please?

When you make a request you are asking FOR something, a service, an object, forgiveness, whatever. It may or may not be formulated as a question.

A question is an interrogation of any kind. The voice rises at the end and it's written with a question mark. It may or may not be a request.

Why is the sky blue? is a question but not a request.
Engmajor's Please take out the trash. is a request but not a question.
Could you hand me the dictionary? is both a request and a question.
I am finally finished pontificating. is neither a request nor a question.