Everything depends on context and personal tastes

Definitions of cupboard on the Web:
a small room (or recess) or cabinet used for storage space
wordnet.princeton.edu/perl/webwn

A cupboard is a type of cabinet, often made of wood, used indoors to store household objects such as food and crockery. A cupboard specialized for the storage of guns is an armoire. As the name suggests, this piece of furniture was originally a simple board or table on which to place cups - recorded use of such a name dates back to at least the Middle Ages. For the last few centuries, "cupboard" has referred to a storage area enclosed by doors.
en.wikipedia.org/wiki/Cupboard

A cabinet, box or closet with shelves designed to hold cups, dishes or food.
www.furnishingsguide.com/glosary.htm

Definitions of cabinet on the Web:

a piece of furniture resembling a cupboard with doors and shelves and drawers; for storage or display
persons appointed by a head of state to head executive departments of government and act as official advisers
a storage compartment for clothes and valuables; usually it has a lock
housing for electronic instruments, as radio or television
wordnet.princeton.edu/perl/webwn