App purchased

You should not have to purchase it again unless you are using a different Apple ID, or something about the app has changed and the developer requires some additional content.

If you purchased the app on the device with the same Apple ID you are logged into now, and you do not have the app on the device, go into your iTunes account and go to Purchases and you should find it to download again.

If you are seeing some type of error message, or something I'm thinking happened has not, please provide a more detailed explanation.

There can be a number of reasons. It could be that the developer requires each download to be a purchase, both on the iPhone and the iPad. If you go to the App Store and it requires a purchase, you can contact the developer with your question, or you can contact iTunes support for a better explanation. https://www.apple.com/emea/support/itunes/contact.html