When you purchase Jump Desktop whether it is for an Apple or Android device, the sale is processed by the respective application store for example iTunes or App Market.
Both iTunes and App Market operate independently and purchases are non-transferable between the two.
Therefore when you have purchased Jump Desktop once for example from iTunes, you can use it for free on all of your Apple devices eg. iPad and iPhone etc.
Similarly once you purchase Jump Desktop from App Market, you can use it for free on all Android devices.
However, you would not be able to share the same purchase of Jump Desktop on your Apple and Android devices and you would have to purchase a copy of the product from each of your devices.