In principle, the same app can run, however the user experience will not be great and will not meet the expectations of the use as the larger real estate on iPad will not be efficiently used.
Also, there are some fundamental differences between the two which have to be kept in mind while developing the applications:
Features | iPhone | iPad |
Phone | Yes | No |
Camera | Yes (2 for video conferencing in iPhone 4) | No |
Screen Size | 3.5 inch display | 9.7 inch display |
Resolution | 960 x 480 | 1024 x 768 |
GPS | Yes | only on Wi-Fi supported Models |
Sensors | Gyroscope | No Gyroscope |
Every app needs to consider the Screen size and Resolution as the major difference. However apps that include phone features, GPS or Camera features will have to be rewritten for iPad.
Also, the lack of gyroscope in iPad makes it not so very suitable for gaming apps.