I was using the Materials Project to look up the unit cell of rutile and they have a useful naming scheme of unit cell conventions:
So they classify:
- input cell (e.g., for DFT codes)
- primitive
- conventional
- reduced (Niggli)
I think perhaps that’s the best wording for our needs, as per @anon86203829 - we call it the “input cell” for the input to DFT codes vs. the primitive or conventional cells.