The Clean button only clears the small Database files.
That's not quite accurate, although quite close. Closer, than my previous statement. The 'Clean' button does sometimes delete some CFA files (which are the largest ones) in Media Cache Files folder. In particular, CFA files related to offline files in a working project. That doesn't change the whole picture though.
Paraphrasing Toomany3, the button should have been called 'Partially Clean Database Randomly'.
P.S. Nope, my previous statement was closer, since I didn't say 'does not', but rather 'may not' (delete cache files for projects other than you're currently working on).