So you know old-school cartoons, like Looney-Tunes and Tom & Jerry? The characters fight, then suddenly Bugs Bunny pulls out a Mallet or something. The “hammerspace” is the magic-pocket that a cartoon just pulls out any item they need without the animators having to worry about continuity.

So I refer the inventory as a Hammerspace because it’s basically a pocket dimension of stuff they have, just with more rules.

And yeah, John’s storage is literally a Hammerspace because it is a space for his hammers.