There is a lot of confusion about the turbo on the Gen III 3SGTE but i have only ever heard of it referred to as the CT20B and we are talking from a long time ago now.....8-10 years.
As long as everyone knows what you are referring to then that's all that really matters...particularly as there doesn't appear to be any other designation for this turbo.
As for it being a different beast to the Surf turbo, most definitely.