These two words have many uses- especially store, so there is a lot of overlap.
I think you come close to a difference with "until you need it again" We stow things we will use again, but we store bulk items to be consumed a bit at a time. Stored items generally will not be returned to storage.
I tend also to think of stow as a nautical term. Everything on a boat must be kept in the most efficient way possible, so some things we might leave out at home must be put away after each use at sea.