The collection option only makes sure the collection folder exists on both devices. You still need to download or sync the books. If the book was bought in the iBook store, just open the store on the iPhone and go to the Purchased tab. You can download previously purchased books to the iPhone for free.
Once on the iPhone, your place in the book should be synced on both devices.
Check out Khan Academy in the App Store for various video lessons you can watch on the iPad.