How did I end up with two iPad apps called Apple Store?
TL;DR: keep the one that looks like a bag, it now a universal app. The cart one was the iPad specific one.

Looks like the one of the left (with the shopping cart icon) is the old one. Launching it now directs me to the new one, but it didn't when I was trying to figure this out before. Here's what I get when launching the old one now.

EDIT-20140917: It appears that Apple may have had a separate iPad app that they have since deprecated and made their iPhone/iPod Touch app a universal app and that's why this app is now defunct.