It also appears that there were some proposals related to SegWit that advocated putting the signatures in a separate block, but the actual implemented SegWit does not do this. Instead it simply moves the signature to the end of the transaction (which allows them to fix most of the malleability issues).
There are many proposals for scaling bitcoin. One of the proposals is to increase the size of the blocks. Segwit also does this by changing how much the signature "counts" as part of the block size. This will allow blocks to be roughly 2mb in size.
Most other scaling techniques can't currently be implemented because they rely on the transaction not being malleable. If SegWit is successful, then these other scaling techniques could be used (but they don't have to be).
It appears that one of the things some people don't like about SegWit is that it was introduced as a "soft fork". This means that it won't be activated in the client unless 95% of the clients support it. Some people feel that this will never happen because some miners are against SegWit. There are also other proposals for fixing the malleability issues and so there isn't a complete consensus about how it should be done (some people appear to complain that the implementation of SegWit is too complicated).
So instead on waiting for other scaling techniques, BCH has advocated a hard fork which increases the block size, but that does not address the transaction malleability problem. Some people have suggested that increasing the block size is the only thing necessary for scaling bitcoin and that other scaling techniques are unwanted.
My understanding is that SegWit will not, in itself, solve the scaling issue other than making a small increase in the block size (effectively doubling it), but that it paves the way for other techniques later (none of which have been decided on yet, but there are working implementations of several).
Is that accurate?