If you really want to be precise, you will need to click all the way through to the very end to get the actual ticket terms and see which sub fareclass you are pricing out, P, I, D, C or J. (Light fare is usually P or I if I recall.) Generally you know it if it's J, because it's quite expensive and I only seem to end up with them on abnormal itineraries. We generally book "flex" fares, and IME I usually find myself in "C" fare. I'm not sure exactly what you mean by "special", but I assume you to be talking about the things I mention below. If you mean things like stopovers, transits, ticket validity, other fees, etc., then you will need to obnoxiously click through and identify your sub fareclass and read the terms carefully, because the English words they use like "flex" or "light" don't necessarily correspond to a fixed sub fareclass.

However, to expand on cxwaterboy's post, CX does not at present offer any business class fare regardless of sub fare class, or their casual English language wording ("light", "flex", etc.) which comes with a reduction in benefits. This trend at other airlines, has not yet caught on with CX (knowing full well I've probably jinxed it.). For example, lounge access, luggage allowance, carry-ons, seat selection, etc. are all the same no matter the sub fareclass you're in. (At least, for now!) That includes award seats too, fyi. I fare, C fare, J fare, Cx award, partner award, all the same. So you can breathe easy. CX treats all same.

CX does give some up-sized modifications for elites, for example guest lounge access, extra luggage allowances, preferential seat selection (in an unofficial way), etc. But it's all upside not downside.