These classes pick up where Fupdate and Fupdate.append leave off and do pretty much the same thing. The difference here is that the form is displayed to the user in a prompt.
In this first example, the form is the same as the example for Fupdate, only I've hidden it (display:none) and then passed it to Fupdate.Prompt so that it'll be used in the popup.
new Fupdate.Prompt($('fupdateForm'), $('fupdateReply'), { stickyWinOptions: { /* this just updates the location of the text over the input */ onDisplay: OverText.update } }).prompt();

This does the same thing as Fupdate.Append, except, as with Fupdate.Prompt the form is displayed in a popup.
new Fupdate.Append.Prompt($('fupdateAppendForm'), $('fupdateAppendReply'), { stickyWinOptions: { /* this just updates the location of the text over the input */ onDisplay: OverText.update }, inject:'top' }).prompt();

Finally, we have two classes that do the same as the classes above, except they fetch their form data from the server instead of the DOM.
new Fupdate.AjaxPrompt('/wiki/simpleForm.html', $('fupdateAjaxPromptReply')).prompt();

Yep. You guessed it. The final class appends data to the target and fetches its form via Ajax.
new Fupdate.Append.AjaxPrompt('/wiki/simpleForm.html', $('fupdateAppendAjaxPromptReply'), { inject: 'top' }).prompt();
