Q: Photosharing between my devices

Yes, with the iCloud Photo Sharing feature!  iCloud Photo Sharing allows you to create shared photo albums that will be available to all devices signed into your iCloud account (and any other iCloud account you manually invite to view the album).  In this case, you could create a shared photo stream, manually add the iPad photos to that album, and then access that album on your iPhone to view/download the photos.  See iCloud Photo Sharing FAQ - Apple Support for setup. 

Note that this is a completely different feature than My Photo Stream FAQ - Apple Support and iCloud Photo Library beta FAQ - Apple Support