Let's not mix whales and turkeys.
TSS was IBM's attempted answer to Multics - built specifically for time-sharing, way too complex, and suffering from second-system syndrome. It never reached product status, but there were a few icustomer nstallations. Bell Labs Indian Hill was one - so that's why TSS was the base of their UNIX port.
https://en.wikipedia.org/wiki/TSS_(operating_system)
TSO was the Time-Sharing Option - by far the most common time-sharing environment for IBM, since it was an add-on to their mainstream OS family - MFT, MVT, MVS, etc. I had the joy(?) of using TSO for my 3 summers with the El Paso Natural Gas company. TSO is the system that earned the 'dead whale down a beach' line from Steve Johnson; it was truly awful. I'm sure there was some TSO somewhere in BTL as well.
https://en.wikipedia.org/wiki/Time_Sharing_Option
The most sane time-sharing choice, and also the best for OS development, was VM/CMS. But for most of its life, IBM was trying to kill VM in favor of the others. AFAIK, there was no VM installation in BTL. See Melinda Varian's wonderful history of VM.
http://www.leeandmelindavarian.com/Melinda/neuvm.pdf