Photos synced using iTunes can not be edited or deleted. You have to make changes in the synced folders or the sync settings, then sync again. The purpose of this method is not to simply copy photos to your iPad, but to sync photos between the iPad and computer; keeping the folders/albums the same in both places.
http://support.apple.com/kb/HT4236
It's best used as a kind of permanent photo album. Something you'd show your relatives, whenever you can trap them in a corner.
Albums created in Photos on the iPad are linked albums. They do not move or copy the photos. Instead you are creating a kind of playlist for photos, for viewing purposes. The original photos stay where they were. Deleting them will delete them from both the Camera Roll and the album.
You might use this to create a semi-temporary collection of photos, perhaps to show your 'trapped' co-worker the newest pictures of you kitten, without having to show them the entire Camera Roll.
If you want permanent albums I offer two choices.
One: A third party app like Photo Manger Pro. On the plus side, you have a lot more control over how your albums are organized and displayed. On the minus side, albums are completely separate from Photos' Camera Roll. They will not be available to other apps, unless you export them to the Camera Roll first.
You can also use Shared Photo Streams. These are albums stored in your iCloud account, shared or not, and can be synced to any of your iOS devices. Unlike the Photo Stream itself, they are permanent. They do not cost you any iCloud storage space; though there are some (very generous) limits to number of photos and albums.
The down side is that they are a bit more trouble to create and manage than the other album types in Photos.
http://support.apple.com/kb/HT5903