Do I have re-purchase a game for Apple TV

If I bought a game on my iPhone and they have that game for apple TV, do I have to purchase again the Apple TV version? are they different that you need both versions for them to work on each device. I can stream my iPhone game but it looks smaller when played thru airplay. Id hate to have to pay again for the same games just to be able toppled it on the apple TV.

any info would be appreciated.