Are trackbacks and permalinks the same things?
Offically no but there's a catch.
You'll notice that the permalink is the exact same thing as the URL for the article in question.
The trackback is slightly different. When you do a trackback, your blog (the one you're writing on) sends back information to the first blog. Sort of a "Hello, I'm linking to you just so you know" message. It's technically called a "ping" but it's different from what a real ping is in computer terms. (But most people know it as a ping or a "blog ping" so you can call it that.)
Now here comes the catch. WordPress can use both as a trackback source. Not every blogging software can. If you were to not include a trackback in your post here at WP.com but include a link in the post, WP will still try to send a ping to that page. On the receiving end, WP will recognize both but, again, some blogs won't.
Good form is to include the trackback anyway just to be on the safe side.
You can find out about Trackbacks here and Permalinks here.
Hope this helps,