BTVI (which shut down in 2019) had no affiliation with Bloomberg TV. It was previously known as Bloomberg TV India but rebranded in 2016.
The one which is being added by Tata Play might be the international version of Bloomberg, or it could be NDTV BQ Prime. If BTVI is being relaunched, it will have nothing to do with either Bloomberg or Adani/NDTV as it owns BQ Prime.