she said it was a root cellar (piwnica)
Well, actually Polish does not map well to English here. Piwnica means usually the lowest underground level of the building.
piwnica = general purpose cellar (but not basement apartment-wise)
piwnica na ziemniaki = cellar for potatoes
piwnica na wino = wine cellar
piwnica na węgiel = coal cellar
piwnica z kotłownią, pralnią = cellar with boiler room, laundry room
Translating from basement in English to Polish gets you to all of the above + suterena.
"Root cellar" has also inconsistent mapping from Polish.
kopiec = mount, knoll
kopiec na warzywa (buraki, ziemniaki) = storage clamp or (less correctly) root cellar
ziemianka = dugout (shelter)
ziemianka na warzywa, owoce = root cellar