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). That's what all of this boils down to, which is why it's laughable that some go around claiming that the want of a quick adoption of segwit with the guarantee of larger blocks to follow is an "attempt to delay segwit".

It's sad that it's often hard to follow the actual facts with so much FUD from both sides.