"Real" diversity are the dimensions that can vary and affect the above context. Different mental models/modes + patterns of human thought can be used to tackle problems in >diverse< and potentially unique ways.
"Fake" diversity are the dimensions that can vary and not affect the above context. Superficial characteristics of a human person will not affect problem solving.
"Fake" diversity can be used as a statistical measure for "real" diversity. A man and a women likely have different life experiences, resulting in different mental models ("real" diversity). A black person and a white person will likely have different life experiences, resulting in different mental models.
Where this all goes awry is when you optimize for superficial diversity. You end up selecting against diversity of thought/character/non-superficial things over time. This sentence is based on conclusions around game theoretic optimization drawn from SSC Meditations on Moloch (https://slatestarcodex.com/2014/07/30/meditations-on-moloch/).