Apple's photo stream has become a little convoluted over the past few years, but once you get the terminology right, it becomes easier to use.  Apple originally debuted Photo Stream as their cloud-based photo sharing solution.  Photo Stream included "My Photo Stream", which uploaded all of the photos you took on one device to all devices with Photo Stream turned on, and "Shared" photo streams, which allowed you to pick photos to share with a circle of friends and family.

And while Apple has moved away from the "Photo Stream" name, rebranding the servcie as iCloud Photo Library, many key aspects remain the same.   

My Photo Stream.  This service has remained the same during the transition to iCloud Photo Library.  Once turned on, My Photo Stream will push a copy of all photos and videos to every device with My Photo Stream.

iCloud Photo Sharing.  This is the same feature as Shared Photo Streams.  It has simply been renamed.  iCloud Photo Sharing allows you to invite a group of friends and family to a shared stream. Once the group is created, you can share individual photos and videos to everyone in the group.

iCloud Photo Library.  The main difference between iCloud Photo Library and My Photo Stream is where the photos are stored.  In My Photo Stream, they are stored on the device and 'pushed' to other devices, where they are also stored locally.  With iCloud Photo Library, photos are uploaded to the cloud and stored there.  This can end up saving a lot of space on individual devices, but there is a drawback: if your device isn't connected to the Internet, you won't be able to view these photos.

 

How to Turn On Photo Stream and iCloud Photo Sharing:

1. Go to the iPad's settings by tapping the Settings icon. Get Help Opening the iPad's Settings
2. Scroll down the left-side menu and choose "Photos & Camera".
3. The Photos & Camera settings will let you turn on iCloud Photo Library, My Photo Stream and iCloud Photo Sharing.
4. If you turn on My Photo Stream, you will have the option to also upload Burst Photos. These are the photos taken when you hold the button down in the Camera app and usually consist of anywhere from 2 to dozens of very similar photos.  It's a good idea to leave this option turned off to save space.
5. If you turn on iCloud Photo Library, you can choose to optimize the storage on the device by leaving all photos in the cloud, which means they will be inaccessible when not connected to the Internet.  If you absolutely must have access to photos when not connect, tap next to the "Download and Keep Originals" option.
6. When iCloud Photo Library is turned on, the My Photo Stream option turns to "Upload to My Photo Stream".  iCloud Photo Library covers much of the same functionality as Photo Stream, but turnign this option will allow you to keep iCloud Photo Library turned off on another devices but still share photos via My Photo Stream. 

How to Get Your Existing Photos Into Photo Stream