Entire difference is, you don't get $this supplied inside the static function. If you try to use $this, you'll get a Fatal error: Using $this when not in object context.
Well, okay, one other difference: an E_STRICT warning is generated by your first example.
In the first class, sayHi() is actually an instance method which you are calling as a static method and you get away with it because sayHi() never refers to $this.
Static functions are associated with the class, not an instance of the class. As such, $this is not available from a static context ($this isn't pointing to any object).
After trying examples (PHP 5.3.5), I found that in both cases of defining functions you can't use $this operator to work on class functions. So I couldn't find a difference in them yet. :(