Difference between "to posit" and "to postulate"

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 quite equal; in some learners' dictionary they're even identical.

postulate/posit: to suggest (something, such as an idea or theory) especially in order to start a discussion

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.

Solution 1:

OED
Postulate: A fundamental principle, presupposition, or condition, esp. one assumed as the basis of a discipline or theory; (also) a proposition that is (or is claimed should be) taken as granted; esp. one (to be) used as a basis for reasoning or discussion, a premise.

A postulate is accepted as true, and it doesn't need to be proven when used as the basis for another argument - it is a fundamental principle and we don't want to be re-inventing the wheel by proving it all over again

OED:
Posit: To put forward or assume as fact or as a basis for argument, to presuppose; to postulate; to affirm the existence of.

A posit, in contrast, is assumed on the basis that it will (hopefully) prove to be true. A possible explanation of how something happened is a posit. If you observe (for example) that economic inflation is occurring, you could posit that increasing wages is driving it, and then set out to collect facts to prove or disprove that posit.