These are all quite similar, and the definitions overlap, so l'll start with a cupboard and a chest of drawers. A cupboard is a cuboid object, with one or more doors on the front which open to access the inside. A drawer is a storage box which can be pulled out of a case. (Drawer being derived from the verb to draw, meaning to pull) A wardrobe is (literally) a place to guard your clothes. Typically there is a tall cupboard with a hanging rail, and some versions have drawers

A cabinet can describe any of these, e.g. a filing cabinet is a set of drawers or a cupboard to store paperwork