I have no answer but I have the same question. First I thought that those variants represent different geoid models but based on documentation they both share the same egm96.grd geoid but way to use it differs:
https://pro.arcgis.com/en/pro-app/latest/tool-reference/multidimension/pdf/geographic_transformation...
BCNS seems to refer only to EGM geoid models so that is only place where those letters are mentioned in documentation. I have had similar issues in Finland and we have simply made assumption that EGM96 represents same geoid model as we officially use and we use height values just as they are without any conversion. So we can assume that EGM96 is same geoid as local official one - just no so rich in details.
This works OK in Finland where terrain is fairly flat and differences are not that obvious. The only place where EGM96 really comes here ahead is some global drone vendors who have decided to use it as a good representation in heights everywhere. Here making conversions through projection tools causes more errors than assuming it represents directly the correct height system. So we simply assume that drone based EGM96 height is equal as local N2000 height.
To me this has come ahead when using DJI Terra software with DJI drones and transferring that data to ArcGIS environment. So only DJI drones are causing me EGM96 issues in Finland.
