I bought an app on one device do i gotta pay for another?

So i bought a game on the ipad with an account. Now on my iphone with the same account it doesn't let me install it.instead i get the price tag and buy the app. Do i have to buy the app again for different devices?

No in the app store go to update then click purchased then click not on this device, all the apps you downloaded should be there

No. You don't have to re-buy them. As long as your signed into the same account on both products (Apple ID).It should just say 'Install'' instead of 'Buy'. Maybe it's just processing? Wait a little. If nothing happens then try contacting Apple. Hope this helps.