Keep in mind that while Wikipedia is good for "general" understanding, it isn't always fully accurate and is never a definitive source for anything since it is user created/maintained. The more technical or specialized the topic (which often goes along with fewer knowledgeable users), the more likely the existence of errors.
For instance, the quoted statement from Wikipedia does go on to list the "six modes" of operation but of the six modes listed, it doesn't include "promiscuous mode" which is referenced in the two or three sentences immediately preceeding the quote. So is this a seventh mode?
Additionally, none of the six listed modes references WiFi Direct, so would that provide additional "modes"?
The "six modes of operation" could be based off of terminology used in driver development. Specifically, the Microsoft miniport driver documentation lists six possible modes of operation.
It also appeas that some Linux or open source drivers reference at least "Master Mode," "Ad Hoc Mode," and/or "Monitor Mode" in some of their documentation and/or correspondence.
AFAIK, the IEEE 802.11-2012 standard only uses the "ad hoc" and "mesh" terminology that are listed as modes of operation in this Wikipeida article. However, it doesn't reference them as "modes of operation" and generally doesn't use them in the same way. For instance, the standard uses the term IBSS (or independent BSS) instead of ad hoc and defines ad hoc as:
Often used as a venacular (sic) term for an independent basic service set (IBSS)