Please answer my question. If package management shares the characteristics of a "store" in that it is the "blessed" and easiest method of obtaining software, what makes it not a walled garden while app stores are?

Debian keeps a minimum imposition policy on their package management. Often they will do the packaging for you even.

In a walled garden, apps are taylored exclusively and you have to do it. They also impose conditions going further than licence and stability. Eventually they ask for a cut of anything you sell over there (which is something Debian hasn't ever done and won't do).

That's where they are going. Stay tuned.