When setting up a new device, it's nice to go back and make sure you've downloaded all of your purchased apps (or any purchased content for that matter), but Google's Play store app doesn't make it easy for this to happen at the moment. Currently your, with no way to separate the two.
After you install the free or Pro version of the app, you grant it access to your purchase history and it will compile a list of your past purchases from Google Play. The list isn't limited to just apps; as it also includes any music, devices, movies, or TV shows you've purchased. You can then quickly view and download the item from the Play store.
Both the free and paid versions of My Purchases will reveal your purchase history. The only difference between the two, besides the $1.29 price point, is that the paid version will remove all ads from the app.