Quite a difference.
Almost all the albums shown on the iPad are ones that Photos creates itself. You're iPhone probably has some of the same ones, depending on what kind of photos or videos you've taken with it. The others appear to be synced from iTunes on the computer.
Mine looks much the same, except I have All Photos instead of Camera Roll and no Photo Stream, because I have different features turned on in Photo's settings. And I've stopped syncing directly from the computer, at least for now.
What method are you using to sync pictures to the iPad and iPhone?
If you are using iTunes on a computer to sync the photos, check the sync settings in the Photos tab for each device, when that device is plugged into the computer and selected. iTunes keeps separate sync settings for each of your devices. Be certain that they are both set to the same folders (if desired), and that those destinations are still valid.
Worst case, turn off syncing for each device and sync (to remove all iTunes synced photos), then re-select your sync settings and sync again. It it's a lot of pictures you may want to re-sync a few albums at a time.
If you are using some other method, let me know. I'm not sure what I could suggest in that case, but I might guess something.