regarding the CT20B, this is a difficult one because nobody seems to have the info.
Toyota brought out a revised range of the bigger CT series around 1996. These had larger inducers and smaller turbine exducers. I was fortunate enough to own a Toyota JZX100 Chaser Tourer V which had a single turbo VVTi 1JZ in it. 377nm @ 2400rpm and 206kw @ 6000rpm !! What an engine, amazing fuel economy also (10.5l/100km around town, auto, 1480kg Sedan)! Anyway, I looked at the inlet and exhaust but didnt remove the covers. (I *think* the 1HD-FTE also runs one of these Turbos. They run out of puff up top though).
I believe it to be what is commonly called a CT20B. Slightly smaller turbine exducer (like around 46-48mm) and the inducer was larger than the Supra CT26, around 47.7mm (I believe that to be the exact number).
All CT26 state that on the compressor cover, but these just say Toyota, that it.
I have a sneaking suspicion that the exducer on the compressor wheel was reduced to around 60mm from the std CT26 65mm, but I do not know for sure
But to answer your initial question, no, dont think cores are the same, and I think the shaft length is shorter in the CT20B than the CT26 by quite a margin, but run the same bearings and thrust washer etc.
They are also Ceramic turbines. This is a good thing in a diesel - my CT26 in the 1HDT was a Ceramic shaft, only because I wanted to prove a theory I had that the "18psi destruction point" everyone talked about in their Supras for blowing the ceramic turbines out the exhaust was predominantly high EGT and or backpressure and or overspeed issue. Well, after 32000km in a year towing a caravan pushing up to 27psi (once to 30psi) and no problems at all. So, I was either correct or I had a rare wheel - I think I was correct

The mods I did was fit a Mitsubishi 18G compressor wheel which has a 68mm exducer and having a 49.2mm inlet, the higher choke flow and larger diameter should keep the shaft speed in check.
Great turbo, boosted like none other factory fitted to any 1H (except 1HD-FTE), but rear housing too small for top end power and the bigger supra housing was too big for the auto. I NEVER experienced compressor surge either. And, the turbo with 270 degree thrust bearing did OK!! I thought it would not destruct because I have an auto, so thrust is not so much an issue.
I have already back cut my turbine to "half way" copy my garrett. Just need to send of the turbo to get the cover and 20G compressor wheel machined up and all balanced. I will do final assembly.
Hopefully the whole process isnt too drawn out...........
By the way, I figure using a wastegate must be more inefficient than backcutting the turbine, fitting an appropriate housing and not using one........