Pretty much. Wardrobes are large pieces of furniture with doors for storage. Closets are rooms (and can be linen closet, coat closet, bedroom closet, etc). Pantry is also a room (closet for food) or a large cabinet for food. Cabinets are millwork/casework built-in pieces.

Although the question sort of reminds me of an interior design professor I had in college that had conniption fits if we used the term "couch" saying those aren't couches they're sofas or settees. The term "couch" was forbidden unless we were referring to a chaise/'fainting couch' which, seriously, who calls them fainting couches any more? (Except Mad Men)