How to edit photo stream? It's different on each device!

Hi, I thought Photostream (iCloud) was supposed to be identical and synchorized between all my iCloud devices

PhotoStream is not a fully synched cloud storage - it is more like a temporary cloud buffer for streaming images between devices. What is kept in sync for all devices, is this a buffer in iCloud, that holds the most recently added images (one month, max 1000 photos). Your devices are holding local copies of this iCloud storage, and the local copies may be holding older photos as well, that are no longer in iCloud. Photo Streams is not syncing all images, that have been downloaded to your devices, only the current window still buffered in iCloud is truely synced. If you delete a photo on your device from the Photo Stream, that is no longer in iCloud, because it is older than a month, it will not be deleted from any local copies of the stream on your other devices.

See this document: iCloud: Photo Stream Troubleshooting

(the paragraphph I see different photos in My Photo Stream on each of my devices.)

You may also want to look at these documents:

iCloud: Photo Stream FAQ

iCloud: How to delete photos from Photo Stream

It is best to delete photos from the photo stream, that you do not want to stream to your devices, as soon as possible, while they are still in iCloud.

I don't have an Apple TV to check, but does this solution work on your device?

HT5125 how to delete from photo stream on apple tv?

I'll try get one of the Apple-TV experts here to look into this.

I don't use Photostream to be honest, but if old photos are shown I would reset AppleTV from the Settings menu and set it up from scratch again - hopefully that will delete old stuff assuming new account details will be entered.

You could also try to log out of the Photostream/icloud account and then log back in and let it repopulate.

One reason I don't use Photostream is that I not infrequently taks pics of documents which there'd be no point having on screen - I think I stopped using it when my underpants apperared on screen - I took a pic of the label to get the product code to buy some more as the shop always had many similar but not identical ones, and you couldn't tell without opening the item!

I don't think there's a 'refresh/reload' stream option but might be worth sending apple feedback as it may be an AppleTV bug as you say:

Apple - Apple TV - Feedback

I have 235 photos in Aperture photostream, 235 photos on iPhone photostream, only 55 on both of my iPads photostream (perhaps explained by the 30 days thing) and hundreds of old deleted ones on my Apple TV photostream. Leads me to think that I was wrong in thinging this is cloud synchronized and there may be a fault with Apple TV (photos not deleting).

Have you tried Alley Cat's suggestion to try to log out of the Photostream/icloud account and then log back in and let it repopulate - I'd try that on each of the devices.

settings > iCloud > iCloud photo settings > turn off/on my photo stream,

Have you also turned the photo stream off on the Apple TVs, not only on the iPads?