There is no "kinds" of segwit. The contention is "what comes after segwit?" On the Core side is "nothing" (i.e., just segwit) and on the "other" side is "larger blocks" (i.e., segwit and 2MB).
Spot-on...
It amazes me how this tiny little difference is creating such huge opposites; it is reminding me on some famous words a president back in 2001 once spoke: "You are either with us, or against us"... I mean, wasn't the current cap purely implemented as a temporarily measure, because back then it was noticed that the chain could be spammed? And sure, we have seen that, yet the chain would only be congested for a few days max...
The current congestion though, is a whole different story in my opinion. The size of the blocks were already reaching their near cap, and when Japan kicked in by officially legalizing the BTC, it got quite clogged; and that's just 1 single country... I think SegWit alone would be enough to unclog the
current situation, but I also think we would be nowhere further than just a few months ago (like, when the blocks were nearly full). So personally, I wouldn't mind to see larger blocks implemented as well, rather sooner than later...