What is the difference between a question and an invitation?
Is there any difference? Do they accomplish different things? Are they structurally different?
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...
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.
An invitation is a statement or question that says are welcome to a party or an event. A question is something which you want answered.
Example of a question:
In this example you expect an answer. "The party is at my house."
Examples of an invitation as a statement:
Here you just make it clear that the other person may attend.
Example of an invitation as a question:
Both are considered invitations but one expects a response on whether or not you are coming.