Good question. I must admit I've never heard of "twin GB" before until you asked this question (at first I thought you were asking about "twinned GB" which is something else).
From what I can tell it looks like another name for a symmetric GB.
I guess there could be a "practical" difference. When people talk about symmetric GB they can also mean e.g. artificial GB which are by no means "perfect" at the atomic scale (there is lots of faceting), when I google "Twin GB" I seem to get a lot of hits where people are discussing dislocations on the microscale in e.g. Si.
Hence, it could be two different names for -what in principle- is the same thing; it wouldn't be the first time different research communities came up with different names for the same thing.
I am curious what someone who uses "twin GB" would call an asymmetric GB?