It's a set.
It shares terminology with the TV/film industry.
The building is the studio. The definition would include pretty much any building with room[s] designed or modified to be used for photography/cinematography.
It contains one or more specific areas constructed for a particular shoot. Each of these areas - whether it's a mock-up of the entire interior of a stately home, or a simple backdrop & a small stand to rest a beer bottle - is a set.
This extends to even when you're not in the studio. Your chosen building or outdoor area is then your location. Any area within that reserved for the shoot itself is also the set, even if no construction was necessary except for lighting.
I think this naming convention is to save confusion for the many people who may not be in the same location two days in a row.
You start at base [which has parking, somewhere to relax, food, hair, costume], are transferred to location & when needed you go to set... wherever it is.