To clarify, if I can:
Photo Stream was initially created as a way of getting photos from your iOS device onto your Mac (or otherwise another iOS device), without having to import via cable, or otherwise email yourself etc.
It worked by detecting when you were on wifi and then uploading photos you had taken into iCloud, in a single "PhotoStream", and likewise, would "sync" these images in that stream to any device you had it turned on, for example in iPhoto, Aperture on a MAc or another iOS device.
It meant I could take a photo on my iPhone, get home and just turn on my mac, and the photo would be there without having to upload it.
These photos were supposedly limited to the last 30 days and like 1000 photos.
in iOS 6 they introduced "Shared Photo Streams". This was basically user-created albums in iCloud that you could get other users to subscribe to, and thus your photos would end up on THEIR iOS devices (or Macs). Thus "the original "PhotoStream" was relabelled as "
My Photostream" to distinguish the "album" that would sync within you r own devices and those that are used for sharing.
Unlike "My Photostream", "Shared Photostreams" are not dependent on time, and are indefinite, but have a limti of something like 1000 photos per shared photostream and like 100 streams or something. That was then, I have no idea about limits now.
Fast forward to today... iOS has renamed "Shared Photostream" to "
iCloud Photo Sharing", but to my knowledge it's the same thing.
As for iCloud Photo Library, this is the new setup that is currently in Beta. It's essentially your entire photos.app library on your iOS device synced to the cloud via iCloud, albums, edits and all. In the future, this will come to Macs as well, and the idea is that everything is in sync. Add a photo by taking it on your iPhone, it appears in your recently added on all devices set to use iCloud Photo Library. Make an edit, such as cropping a photo on your Mac, it crops it on all your devices set to use iCloud Photo Library.
There you go, clear as mud
In summary:
"My Photo stream": time-based temporary album of YOUR photos for YOUR devices, set up to provide an easy way to move photos between your devices.
"iCloud Photo Sharing": albums you create and have others "subscribe" to, so that any photo you add, subscribers see them immediately, and can comment and like.
"iCloud Photo Library": the new fancy, complete syncing solution between your own devices of all albums and edits. Still in beta.
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As for your question, none of these are for backup or archival purposes. "My Photostream" is supposed to be temporary. "iCloud Photo sharing" is for sharing, and I don't think it uploads full-res files for sharing. iCloud Photo Library WILL keep the full-res file on record, but it's technically not backing it up so much as offering a cloud storage solution. For example, if you delete it on your iPhone, I assume it sits int eh "recently Deleted" album, but when removed from there, that removal syncs across all your devices. I haven't looked too much into iCloud Photo yet.
The proper "backup" is off loading them to another storage solution (even if you use "My Photo Stream" to achieve the move, for example, using photo stream to see the image you take on your iPhone to be seen on your Mac, and then importing it from "My Photostream" on the Mac to your iPhoto/Aperture library (these apps can also set it up to do it automatically).
In addition, iCloud Backups are set by default to include your photos in its backup.
