This really is irrelevant, true or not. Just look at the technology. Bitcoin Cash is what the design paper presented and has a lot of the great early developers involved.
Bitcoin "Core" or "LS" can work out just fine. Lightning Network can become the go to solution and the LS chain is not used except for settlement, or perhaps at some point the chain becomes useful for regular transactions for good again and then there might be two great coin projects developing simultaneously.
We'll have to see what happens.
I believe Bitcoin Cash will scale soon. It has already been tested safely at 7,000,000 tx's per second. It's the only blockchain that can scale that way. That's faster than Visa. Also faster and more scalable than Nano, Ripple, Steller, etc
As far as lightning, implementation is a long way off. And, time waits for no man. What did you mean by LS?
Agreed. Bitcoin LS (Legacy+SegWit) is the "Core" blockchain alone, not including the Lightning Network.
I see. Yeah, different people call it different things now. I call it Bitcoin Segwit sometimes because it is a segwit fork.