Understanding the 'void' between C1 & C2

As serious ESLL'ers know, a C2 certificate is the pinnacle of achievement. Nearly everyone dreams of holding a C2 certificate in their hands after years of struggle and work. But...many don't realize that the gulf between being at the C1 level and being a C2 speaker is...LARGE! There is a similar gulf between being a B2 learner and a C1 learner, but not nearly as large as between C1 & C2. First, what IS a C2 level - often referred to as Proficient or Upper Advanced, depending on the language institute's nomenclature, in relationship to IELTS or TOEFL standards??