Or in another words: if I have two different links generated when shortening a Twitter message, does it surely mean that they point to two unique addresses?
Not really, here are three t.co links pointing to the main Stack Overflow website and all of them have different URLs.
http://t.co/Ys1GFWI7 http://t.co/BoUuFo3s http://t.co/tdFXxGti
As Amit says, t.co links are not created based upon the target link.
This is true of all (I think) URL shorteners. A good example of this is bit.ly, which allows you to create links and tracks their analytics.
For instance, if I shorten this page's link to: http://bit.ly/Xk0DDl then I can add a
+ to the end of the URL and be taken to a page for this link's stats (http://bit.ly/Xk0DDl+). This would not be as relevant if all URL shorteners created duplicate URLs because they shared the same targets, and thus the same stats.
Likewise, it would require significant resources to be able to index, track and re-use t.co links based on their target destinations.
Now, in the case of t.co, I don't believe you can access the link analytics in the same way, but the same principle applies about it being difficult to track URLs and grab the already-used links.