Notifications on iOS devices: most (but not all) iPhones are now running iOS 4, but iPads are still using a version of iOS 3. The two versions of iOS have different approaches to notifications. When running on a device OmniFocus (both editions) will use whatever features the OS supports.
Now: more detail. :-)
On an iPad (or an iPhone with iOS 3 installed) OmniFocus does not have the option of presenting an alert without some sort of external server. When running on one of those devices, OmniFocus can export a calendar file to your iDisk (or another WebDAV server) which contains info about all your actions' deadlines - every time you sync, the file gets updated.
OmniFocus then tells the Calendar application on your iPad or iPhone how to subscribe to that calendar file. The calendar application presents alerts to you. (Apple gives their own applications access to code that OmniFocus doesn't get. On iOS 3, the calendar app can present alerts that we can't.)
As you may be thinking now, this setup seems kind of complicated and less-than ideal. You might hope that Apple would make things better. Well, in iOS 4, they did!
Applications running on iOS 4 devices have access to a new feature called "Local Notifications" - essentially, all apps can now do what the calendar app was doing on iOS 4. When OmniFocus is running, it tells the OS about your upcoming event deadlines, and then alerts appear. No server export necessary.
So, the rundown:
OmniFocus for iPhone: does whatever it the current device supports. IPhones can run iOS 3 or iOS 4; either set of features will be active depending on your phone.
OmniFocus for iPad: iPads currently run a version of iOS 3, so it only does the calendar export. Once iPads support iOS 4, it will behave like the iPhone app and do whatever the current device supports.