Learn English – Difference between “get” and “take”

The only real justification for seeing dialog as "American" is that there are many words where US spelling seems more "logical" than British - largely thanks to Webster, though so far as I know he never addressed this particular issue.

Paraphrasing grammarist.com's entry on another such word: all early editions of Noah Webster’s dictionary list catalogue, but by the 1890s catalog was commonplace in AmE texts (Webster often gets credit for changes he played no direct part in).

There aren't many written instances of dialog prior its rapid uptake by software-oriented writers, but here's one from 1910 Transactions and proceedings of the American Philological Association, where one might reasonably suppose the author to be perfectly literate.

I think it's just that on average people involved in technical writing are more inclined to ignore precedent and go for what seems to them the logical spelling. Consequently we see the short form much more often in computer contexts such as dialog box, leading many people to suppose there are in fact two different words involved (or at least, that the word has two different spellings dependent on context).

It seems to me usage is currently in a "transition phase", but most likely the shorter form will continue to encroach further into traditional, non-computer contexts, and will eventually be seen as standard for all contexts (but for most people, particularly Brits, this hasn't happened yet).

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.