One difference is (at least with alternate app stores on Android, and I assume it'd hypothetically be the case on iOS), regardless of where you install a mobile

One difference is (at least with alternate app stores on Android, and I assume it'd hypothetically be the case on iOS), regardless of where you install a mobile app from, it appears on your app drawer/home screen. You don't have to go through a specific launcher for each store/platform as you do with Steam/Origin etc. (I think... been a while since I've used any of them). So in most senses, it may not "matter" where you bought it from (assuming all app stores can do auto-updates or notify you of available updates etc.)