The iPhone version includes improvements to in-store alerts that allow users to view notifications both in-app as well as on the lock screen. Apple's deployment of in-store iBeacons is a major feature for the Apple Store app and it looks as though the company is taking the implementation a step further with this release.
As for the iPad version, users can now purchase Apple Store Gift Cards in any denomination from $25 to $2,000. Physical cards will be mailed out, while digital gifts are sent via email within 24 hours. The iPhone app already includes this functionality.
The Apple Store app can be downloaded for free from the iOS App Store, with the iPhone version coming in at 6.8MB and the iPad version at 23.6MB.