The interbinary flag and definition was submitted by an anonymous person, so hopefully they can give a better explanation! From my perspective, though, I can see some difference between the two.

Ultergender: intersex people who identify as a gender other than their assigned gender at birth, but do not feel the term “transgender” describes them, because of being intersex

Interbinary: intersex people who are sex/gender dysphoric but feel like they don’t belong in transsex/gender spaces for whatever reason; not a gender.

It appears that ultergender is specifically for those that feel their gender is not their agab, but that they are neither cis nor trans due to being intersex. This doesn’t mean they are dysphoric or non-dysphoric, however. 

Whereas, interbinary seems to be for those that are dysphoric, but still don’t consider themselves trans due to being intersex. It also doesn’t specify whether or not the intersex person who considers themselves interbinary would be identifying as their agab or not. So, following this logic, as interbinary is an adjective, perhaps an intersex person who is dysphoric but still identifies as their agab may identify as interbinary cisgender? An interbinary man or interbinary woman. 

That’s my take on it, from comparing the two definitions. 🙂