Yes, it could be either – if you mean free-standing vs built-in. It can also refer to 'someone's entire collection of clothes'. It's en garderob btw, Doge. A big closet can be en klädkammare, but real estate dealers love to talk about en walk in closet in Swedish too these days.
It accepts that in several versions. A common answer we don't accept though is The wardrobe has no door since singular/plural works pretty much the same in English & Swedish here so there's no good reason for switching. Other than that I don't know what could have happened, it should accept wardrobe.
Indeed, in America you can keep cleaning supplies, office supplies, clothes, etc. in a closet. Fun fact, though, if your kitchen has a little room about the size of a closet but it's where you keep you dry goods (flour, canned goods, boxes of cereal, etc.) we call that a pantry.
Garderobe was the term for what passed for indoor toilets in castles. They were a tiny room that bumped out from the outer wall above the moat or just the ground with a seat with a hole open to the outside. I have to always remind myself that a Swedish garderobe serves a very different function. :-)