ct20 is the name of the turbo. No 'b' after. If you go to toyota they can look uo the ct20 on their computer sustem.
Ct20 is a beter turbo for a near stamdard gen 2 3sgte.
I has a larger exhust housing and is slightly larger. It can compress more air and hold hihger boost far more efficiently.
I think that you are on your own with this statement.
As JustenGT4 has pointed out; there needs to be clear differences in the naming of the turbos.
If you go into a wrecking yard and ask for a CT20 turbo, then what you will get is not guaranteed.