Links there are shortened versions of a full link, with a reference to your user ID. For example, your question is:
For my account, the permalink for the above is:
/q and takes out the text at the end (the "slug"). If you're logged in, it will also append your user ID for Announcer, Booster, and Publicist Badges. If you don't care about that, or want the link to be anonymous, then remove your user ID:
Both versions of the permalink should be permanent as long as you don't delete your question.
The same applies to answers, showing an
a instead of a