"Bitcoin Classic" is actually the name of one of the software implementations of Bitcoin, which can be found here: https://bitcoinclassic.com (ironically it supports both the unforked chain and the forked chain, Bitcoin Cash)

I prefer to refer to the unforked Bitcoin chain as "Bitcoin Original", or "Bitcore", "Bcore", or anything other than "Bitcoin", really, because it becomes less like Bitcoin the more days that pass.

+1 for your post