Here in the UK it's pretty much cupboard for everything. Airing Cupboard, cupboard-under-the-stairs, kitchen cupboards. Nobody really says closet here, it's always wardrobe, or walk-in-wardrobe or built-in-wardrobe.

My Granny had a pantry in the big old farmhouse my Mum grew up in, but it was actually a narrow, long room with stone flors and slate shelves where she...well hoarded everything that might come in useful, as well as food! And although I realise that I said 'cabinet' up above, we actually call it a sideboard in our house! Iwas trying to think of the word, sorry!