My Photostream was a syncing system that is giving way to iCloud syncing. iCloud syncing transfers pictures from the to the "Cloud" and then from the Cloud to the Mac, back and forth. You can go to iCloud.com from any browser anywhere and see all your pictures, and all your devices keep in sync pretty much effortlessly. If you have lots of pictures, you would need to pay Apple a bit for the storage space in iCloud ,like $3/month for 200GB. It's pretty cool.
So, check iCloud.
Set up and use iCloud Photos - Apple Support
Optimize Storage means that only smaller, screen-sized images may be stored on you Mac (and a similar setting for the phone). The pictures look as good as they can look on the screen, and when you want to edit or print them, the computer brings them in for full resolution. You usually have to be connected to the internet to edit or print. I have plenty of room on my Mac's hard drive, so I don't check this. That way, when I back up my Mac, I'm backing up full sized images. Of course, the full sized images are alway in iCloud.I do have it checked on my phone.
Shared Albums lets you make pictures available for friends and relatives who use Mac Photos. If your interested, you can look here:
How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support