I've googled how to identify "wall storage type," "hook type," "attachment type," etc., and all that EVER comes up are slatwall and pegboard, which look nothing like what I have.
The metal piece that is horizontally attached to the wall has two rows of hollow, vertical slots. A single hook/attachment piece has matching two rows of "hooked prongs" that slide down into wall slots (four slots/hooks each). I'd hate to spend money on something new if I can't find more attachments.