not a definitive answer, but perhaps a reasonable hypothesis ...
\varnothing is shorter than \varemptyset. mathematicians aren't generally great typists.
although \varempty is even shorter, \empty, while not a primitive, has quite a different meaning, and a "var" of that would only be confusing.
"the joy of tex", while it mentions both, has nothing useful to say on the matter (sorry, must be on auto-pun this morning), and in fact doesn't even point out that they have the same meaning.
the control sequence \nothing does show up in cjwmath.sty, where it is equated to \varnothing, and there is a further alias, \leer, for \nothing. i didn't find this name anywhere else in any package on tex live.
so the reason, to me, is lost in the mists of time.
i suppose i could ask mike spivak.
i have consulted the documentation for the composition system used at ams prior to tex. the name given to the slashed circle is "null set", for which a "short name", empty, was assigned for use by input keyboarders. (the system was highly encoded, and the canonical code was *yo; keyboarders were free to use whichever form they preferred, i.e., more easily remembered.) so the term "nothing" was not in use at ams in any relation to this symbol prior to the creation of the ams symbol fonts.
what would be in those fonts was defined by a committee; i've sent an inquiry to one of the few surviving members of the committee in the hope that he remembers.
i did ask mike spivak, and he doesn't remember, except that he's pretty sure he wasn't responsible.
i have found the definitive release notice of the original ams extra symbol fonts in the july 1985 issue of tugboat. these were the msxm and msym fonts, and initially (and erroneously) referred to as "euler", a lapse corrected in an update later that year. the name \varnothing is used, however without any commentary on choice of names. (and, unfortunately, the page in the scan of the update that would show this symbol is missing; but i've confirmed its presence in the paper copy on my bookshelf. i'll try to get the posted copy on the tugboat web site corrected.)
Best Answer
\marks is an etex primitive command. It extends the \mark command of the original tex. You can use it to store text on the current page which you want to use at shipout in the headers.