First of all, I think are two different sets of things, say the utility closet to put all cleaning supplies inside, along with brooms, mops, buckets and other tools.
As for cups, bows, plates, you could call them "items" and you would certainly store them in a cupboard or cabinet. To store food suplies, chances are that you use a pantry.
The definitions vary because space designers are creative with language. You can run a search with Google Image, though.
Off course you can say "that where I organize/store my stuff" but it´s a generic way, it would be a good thing to learn the name of those things. Doing that you build up vocabulary and make yourself better understood.
This is a kick-off answer, natives can polish it further, and may be more accurate.