CSW and bitmain aren't long term partners, but they cooperated long enough to stop core fucking Bitcoin forever more, so it was a good partnership while it lasted.
"Core" is "Bitcoin". NOBODY else in the entire cryptosphere calls it "core"! The entire world agrees upon this other than those who decided to invest in the altcoin bcash and potentially its spinoff, now they're protecting it with religious zealot fervor, even after weathering 80%+ losses.
As many rational minds have stated, if Bcash wanted the least bit of respect, they would change their name to something other with "Bitcoin" in it, and stop trying to win support through confusion and non-stop attacks on bitcoin.
You obviously move in other parts of the cryptosphere to me, I see neutral people referring to 'Bitcoin core' all the time, to distinguish it from 'Bitcoin cash'. Neutral people don't take sides, and the history of the split from my point of view is it's far too early to know what the eventual outcome will be, but btc and bch can both use the name 'bitcoin' because they share the same genesis block. Which version is closer to the original and therefore has the best claim to Bitcoin name is an opinion, not a fact, so for now both should use it, but add meaningful word after Bitcoin to help distinguish them. Only zealots on one side or other would disagree, probably to stifle honest discussion.