Apps that have a plus sign next to them are Universal - the same application is compatible with the iPhone and the iPad. If you own one of these apps, you can use it on both types of device without paying again.
Some apps, however, have separate iPad versions. These are completely separate from their iPhone counterparts - they may as well be completely unrelated as far as the App Store is concerned. If you own the iPhone version of an app, and there is a separate iPad version (no plus sign), you must buy the iPad version in order to use it (of course, you could always use the iPhone version on the iPad, but it won't have the iPad-specific interface).