You find yourself half way between Tokyo and Rio de Janeiro; about as far from Mexico City as from Moscow.

Albert Einstein waits to the left, ready to explain his theory of relativity. A short distance to your right James Watt hopes to recount his development of the steam engine to you. John Steinbeck and Isaac Bashevis Singer crouch over you, vying for your attention.

Your surroundings are conventional and functional. One aspect stands out: A piece of furniture - represented in 2 or 3 specimens in the typical home - recurs here hundreds of times.

What are the two common names for this item of furniture?

Coming late to the replies, might I suggest that a more "common name" for the library furnishings (with the books) would be the "stacks" -- with perhaps "bookcase" for a small isolated unit, e.g. between two windows, or in a rare books room (in a library context, I think the term "case" would suggest enclosed shelves, vs open stacks -- which might mean either unenclosed, or accessible to the public). I think it odd indeed to refer to a sizable library as "bookshelves" though one might refer to the collection generically as "the shelves" (e.g. "go, check out the shelves...").  It would be a rather small library, public or otherwise, which (in the unlikely event of shelving nonfiction by authors) would have the entire alphabet in a single room -- and "card" in the title (though not in the text) suggests an institutional setting.  There may be regional/national nomenclature variances as well.  I suppose if your were thinking of purchasing the units, you would ask for (library) shelving.