In US a wardrobe is a collection of clothes-- (i have a large wardrobe--I own over 20 skirts!) and occationally would be used by grandparents to define an Armoire-- a large free standing piece of furnature to hang clothes in.
cupboards-- is used (but pronounces closer to cub birds)--but mostly cabinet is used (i have new cabinets in the kitchen, ie,) and a free standing kitchen cabinet might be a hooser-- a cabinet with short legs, (6 to 8 inches) topped with a storage space behind 2 doors- on top of that, two deep drawers. Then there would be a work surface-- sometimes covered in tin. above the work surface, some more cabinets-- shallower then the ones below-- Some hoosers had one cabinet above, and to one side, a large built in bin to store flour-- at the bottom of the bin-- a built in sifter-- the sifter would deliver the flour to the work surface. the whole thing would be about 5 foot high-- sometimes a little higher-- but never more than 6 feet high-- and about 3 feet wide, with a depth of about 20 to 24 inches. They could be very ornate-- with fancy glass in the panels on the doors of the upper cabinet.
Old ones are very popular now-- and very expensive!
If you are lucky-- you might have a pantry in your kitchen-- or near it-- Like the cooler WoW mentioned in an other thread, it was a large (floor to ceiling) area-- sometimes big enough to walk in--with shelves for storing dishes, and food items. Country homes often had a root celler too, (my first house had an old Coal room-- from when the house was heated with coal- it had been retro fitted with a gas fired boiler (for steam heat))
Estate house's(mansions) would have a butlers pantry-- a room half way between kitchen and dining room (sometime part of the passageway/hall way between the rooms) that has many shelfs for dishes, serving pieces, silverware.
I heard of a press-- and knew it to mean a kind of closet-- but i never hear the word used here-- (press is a verb-- to iron, and Presser would be a person who has the job of ironing (say at a large commercial laundry).
Under my stair way is a trianglar storage area-- its a closet--of course! I keep my brooms, and mops, and cleaning stuff in a broom closet, too.
