It is a more subtle use of -게, but you can think of it as an extension of meaning (a). In the sentence, 크게 is also used similarly, as in 크게 나뉜다 if you simplify it. 다르게 나뉜다 is not that different, except that it does not work as closely on the verb as 크게 does. You can think of it as a loosely connected adverbial phrase. In texts, 달리 is probably more common in this context, but the two are essentially the same in meaning and function. 다르게 can be translated as "unlike", "in contrast with", "as different from" or something similar. - 한국에서는 서양과 다르게/달리 이름을 성부터 쓴다 = In contrast with Western practices, you write your surname first in Korea. - 작년과 다르게/달리 금년에는 비가 많이 안 온다 = Unlike last year, it isn't raining much this year.