I am using the material from the Common European Framework of Reference but the following interpretations are mine.
The early, A1, A2, and B1 levels seem to be defined by quantity of language knowledge, and the later levels, B2, C1 and C2 by quality.
A1, A2, and B1 refer to mastery of common and everyday language. An A1 knows only a few words and phrases, typically about identifying and introducing people, time and location, weather, etc. An A2 knows "many" words and phrases, and a B1 knows "most" words and phrases in everyday, common use. A B1 is more practiced in the language and has better control of grammar than an A1 or A2, but may still have some difficulty or discomfort in getting around, even though s/he is capable of it.
The paths seem to diverge at B2, where some "expertise" is expected. One kind of B2 is a "super B1," who is more fluent and spontaneous with everyday situations, with a broader knowledge of vocabulary and grammar than a B1. The other kind of B2 is developing expert skills in a narrow field such as business, science or law (usually the profession or area of interest), even while not being fluent overall.
The paths converge again at the C1 level, where one gains the other skill (either greater overall fluency or expert knowledge). A C2 is basically a "complete" and fluent speaker of the language, with maybe slight weaknesses of accent or idiom preventing them from being a fully "native" speaker.