As it says, it's a stream. It is for those people who want every photo they take to be available on all their devices and computer, at least long enough to copy them to a more permanent location. Photos only stay in the stream for 30 days or 1000 photos. It is not meant for organizing. You do that by copying the photo to the iPad, or some other app or service.
If you don't want what it offers, as you said, turn it off.
It would be nice to be able to manually force a photo into the stream, or remove one that you find annoying, offensive, or possibly incriminating. Hopefully that will come in the future.
In the mean time all you can do is reset the entire photostream; removing all the photos there.