It is true that BCC will be a continuation of the original chain, and it is also true that in some substantial sense bitcoin cash can be said to be a continuation of the original bitcoin blockchain and incentive model to a greater degree than bitcoin core will soon be, as bitcoin core moves over to segregated witness with a "block weight cap" rather than "block size cap".
I therefore rate MichaelBurge's sentence "BCC is not actually a fork but is the original chain/software, isn't it?" as false (it is a fork), true (it is a continuation of the original chain), and true (it is a continuation of the original software).