Some UI hints that may help:
Ellipses and Arrows
Historically, Ellipses have been used to indicate the presence of a modal popup. Example: File->Print... indicates that a dialogue box will open for the user. Ellipses would probably suggest an AJAX action.
Submenus are usually hinted using arrows.
If the page is meant to represent a single record but the record has information divided into different groups, the groups may be represented as tabs. Since all of the data is part of a single object, it is expected to load without refreshes.
Some of the stackexchange websites use tabs to represent different sections of the website. The sections are not part of the same document / object, and so are not expected to load without refreshes.
The default unstyled submit button has had a long enough history with full page refreshes that "Submit" by itself should probably suggest a page refresh. I don't think the converse is true, though.
Multi-part forms usually have buttons that indicate a final action, "Submit", with buttons before that for "Next". From the user's perspective, you should be able to "take back" the "Next" action before the final Submit. Refreshing gives a sense of finality to it, so you probably want "Next" to be in Ajax.
Applications like twitter and facebook that have a dynamic Ajax stream suggest that the submit button is also Ajax. In both applications, the button "activates" only upon entering text into the feed interface. A visual suggestion that the button is linked to the stream is also helpful. With twitter, there is no other place for your posted data to go but the central stream. With facebook, the post button is placed immediately above the stream, looking like an element inside the stream itself. In both, the color of the activated button looks like the links in the stream itself.
I'm not sure how this applies to stackexchange's "post your answer" button. The plain styling and finality of the wording suggests that the page will refresh, but the presence of the post textarea in the stream suggests that the text will appear in the stream shortly.
I'll post and see which it is .