After rumors of a revamped app, Apple has now updated their Apple Store app with a new icon and For You section. With this update they have removed the Find a Store tab and put that inside the Shop section. Most of the information on stores can be found there, but things like the free Apple Store app of the month can be found on the main Discover page.
The Discover page will show you recommend products and things that you might be interested in. The Shop tab features pretty much all of the same information, as well as the device tabs nested inside. We still have an account tab where you can see information about your orders as well as a bag tab next to that to view your cart.
You can update the app from the App Store now or download the app for the first time from here.