Well. Probably it is just a translation refuse. Let me explain:
The original name of the "Great Monkey" form is
猿 or Saru (the s becomes a z due to a rule called "rendaku" - see here, link courtesy of Pleiades.) means Monkey. The or Dai character instead just seems to mean "big/large".
(As to why the name is transliterated into Ō-zaru instead of Dai-zaru I have no clue. I know that Ō is an honorific form, so the term could also be interpreted as "Honorable Monkey", but I have no further clue).
So basically the translation of the name would just be a generic
which does indeed fit the "monkey king" theme.
Also worth mentioning is that Sun Wukong did indeed had a tail (even if it is not so prominent in most of the historical painting featuring him): that was a problem for him since one of his weakenes was that the tails often did not fully transform, limiting the forms he could assume because of this. And unsurprisingly enough - the tail is also a weakpoint for saiyajin too.
Anyway, back to the question.
I sincerely doubt whoever made the translation had in mind the difference between apes and monkeys at the time (see here), so he probably just picked the word that sounded best (also worth mentioning is that probably it sounded more intimidating). What really matters here is that the Japanese name does not seem to specifically refer to just apes.
Also, I suspect whoever made the original translation just though "this is King Kong"... and since King Kong is an actual "giant ape"....