The main difference is that if you ask a question, you require an answer. If you post a question and no one replies to it, your post will appear under the 'Do you know the answer?' feed on the home page.
"Questions" also provide the ability for others to vote up, or suggest a helpful answer and, as the original poster, you can mark a reply as a "Helpful Answer".
Posting a "Discussion" means that you don't require an answer, but want to start a conversation with other community users that doesn't require a resolution to an issue.