What exactly is the difference in meaning between the two words posit and postulate, besides the fact that the latter one is also used as a noun?
Both words are formal and their definition are quiet equal; in some learner's dictionary they're even identical.
Based on COCA both words are commonly used with theory but postulate is the appropriate word for Khazzoom–Brookes postulate. But since both words posit and postulate are not very regularly used this is the only hint the corpora gives (and BNC contains even less material).
It doesn't look like there's a general tendency to use one word more commonly for a particular area of expertise, for instance science(e.g. astronomy) or religion (existence, God), except the Khazzoom–Brookes postulate, of course. At any rate, it seems like the words can be interchanged.