Learn English – the difference between “synergistic” and “synergetic”

Output is usually used to measure the rate of something. It is often used when talking about energy/power created.

Outcome is the result of an action. The outcome of a fight, for example might be a couple of black eyes.

To try to put these into one context:

This book was the outcome of three years solitude and constant work from the author.

The author has an incredible output, having released 5 books this year and 6 last year.

Also,

The outcome of increasing the machine's printing speed was a much higher output.

Here, by increasing the speed, the engineers have improved the efficiency of their machine.

Hope this helps.

N.B.: It has been pointed out in the comments that output can also be the result of running a process in some computer applications and data processing.

I realize that Stephen's answer is pretty thorough, but can't help but think that side-by-side comparison of their definitions may help a bit, so...

Question: Noun: A sentence worded or expressed so as to elicit information.

and

Invitation: A written or verbal request inviting someone to go somewhere or to do something.

So the answer to your question "Do they accomplish different things?" is "Yes". They do. question is for obtaining information, and invitation is more for giving information.