Better Inventory System Needed

@dopaminedroid I never considered that chests might share a single inventory if you don't use mods for them. I've used coolspear's storage mods for so long, I may have forgotten what some of the 'features' it adds are.

I checked his mod description and it seems to imply that you are correct, default game behaviour shares storage across the chests. This is from the mod description; I bolded the part that seems to indicate you are correct regarding non-modded game behaviour:

The purpose of the Personal Storage mods here is to open up many objects in the game to have a new kind of storage facility that does not exist in the game.
Firstly to offer a unique storage hold for each object, so that it can hold absolutely anything inside which a sim can normally hold in their own personal inventory. No restrictions, If a sim can hold it, so can these objects. Secondly, to make each object its own private storage space, so that what you place inside one, will never be available when opening another. This is not Resident Evil, we don't want to find the same stuff in every storage box we open. And lastly, for this set in particular, to give each item the Live Drag function so you can drag the objects in and out of a sim's inventory, or command the sim to "put in inventory" or "place in world." So that our sims can carry them everywhere for quick storage use and access wherever they may travel.

That's unfortunate, as it certainly makes the storage chest much less useful for folks who are not willing to use mods.