Changing permalink url of one post only. What will happen?

For a really complicated reason (trust me, long story), I have to change the permalink of one specific post on my blog.

The thing is, this post is interlinked dozens of times throughout my blog, has a bunch of awesome external links pointing to it, and ranks really well in search engines.

If I change its permalink url, what will happen? Do I need to set up a 301 redirect or does wordpress somehow take care of all of this on its own?

Assuming wordpress may be able to take care of things on its own, is there any difference between changing the url from this:

original: http://www.domain.com/this-is-a-cool-post-about-stuff/
to this…
new: http://www.domain.com/some-new-title/

or changing it from this:

original: http://www.domain.com/this-is-a-cool-post-about-stuff/
to this…
new: http://www.domain.com/this-is-a-cool-post/

Any help would be greatly appreciated. Thanks.