Adding to Poser's reply, if the app has a "+" mark under the price, this means that it is a "Universal App" and can be used on both iPad and iPhone for one price. If not, you may have to purchase two separate apps *if* they are available for both devices. Some apps are only for iPhone and some only for iPad. It's case by case.
If you were asking this from a financial perspective - i.e. do Apple allow me to download the same app to my iPhone and iPad the answer is 'yes' if both devices share the same iTunes account.