Are invisibility cloaks simply 'rare' as Ron says or is Harry's cloak unique and proof?
It’s the second one.
To be clear, invisibility cloaks are extremely rare. In Order of the Phoenix, the Order gets in a bit of trouble when Sturgis Podmore is arrested since he had Mad-Eye’s back up the cloak. Both the fact that no one else has a cloak and the fact that Mad-Eye isn’t willing (or expected) to part with his other cloak indicate that these are rare.
However, Harry is clearly different. As soon as the trio hears the story of the Deathly Hallows, both Ron and Harry immediately make the connection, and Hermione is intrigued but cautious as well. Unlike other cloaks, Harry makes you entirely invisible, and it doesn’t wear and tear the same way a normal one does. The only reason the whole trio isn’t immediately certain is due to the fact that they aren’t certain of the Hallows’ existence; if that is confirmed, Harry’s cloak is clearly the one.
Ultimately, these points were cut from the movies (unless I’m going crazy), so I totally get the confusion with it. Still, in the books, it’s firmly established that Harry’s cloak is noticeably different, which is what establishes its status as a Deathly Hallow.