IOS – Why is Photo Stream not visible in iOS 12

Photo Stream definitively only works for photos (or screenshots) taken after it was enabled.

As for your other problem: Yes, if you are logged into the same iCloud account on both devices and have Photo Stream enabled it should sync whenever you are logged in into a Wi-Fi environment (apparently Photo Stream doesn't sync over 3G).

What else can you try:

• Take a screenshot on the iPad, make sure you are in a Wi-Fi environment and see whether the screenshot appears on the iPhone
• Log in to iCloud from your computer (requires Lion or a recent Windows version of course) and see whether the photos get streamed there

Photo Stream only saves either your last 30 days' worth of photos or your last 1000 photos, whichever you hit first. However, in iPhoto on the Mac, the "automatic import" feature (which I believe is enabled by default) will automatically copy any photos in your photo stream to your Mac's local hard drive.

So I think selecting "Photo Stream" in iPhoto shows the temp store, but they are also saved into a Event where they will remain even after being removed from Photo Stream.

Correct (again, as long as you have automatic import enabled. You can double-check the setting in iPhoto preferences).