Some iPhone apps are not designed for iPad but can be scaled up. Some are available on both free, or paid once and Ok for both. A few have separate pricing for each version. When you buy (or get a free version) for one it will automatically authorise the iPad version to iTunes if it is allowed
My husband has quite a few apps on his ipad some free some paid for they get saved into itunes when you sync the ipad. He recently got an iphone and all the compatable apps were installed onto the phone when it was synced with itunes. So no he didn't have to buy them twice.
Just log in to itunes or app store on the other device in the same account (name and password) as your other one and download it again,It won't charge you even though at first you click on it and it says the price.
When you open up Itunes, go to the ITunes Store tab in the list on the left of the screen (above your Playlists). Click on it, and on the right of the screen you see 'Purchased - New'. This allows you to download any Apps/IBooks that you have purchased on your IPhone/IpodTouch/Ipad onto your computer.
Some apps can be installed in several devices and need to pay only once, such as iPhone WiFi Transfer, Video Converter App, etc. Youc an find them on the App Store.
http://iphone-to-computer.com/