Hmmm. These words are used differently here in Québec, L.J.

A cabinet is either;

1) a free-standing movable piece of furniture with drawers or compartments used for storage of household things - usually things important to you.
2) as you mention, storage compartments attached to the wall in the kitchen for placing dishes.
3) a doctor or lawyer's office
4) the group of ministers in the parliament.
(in French it is also used to mean the toilet room)

And a cupboard is always a storage space with a door, the size of a closet with shelves to store kitchen stuff (non-perishable foods, pots and pans, etc.) I've never seen cups in a cupboard. Those are always in the cabinets.