Sharing Photos between two separate iCloud accounts

Hello,

The iCloud Shared Photo Library would be an easy way to create a combined library from two different personal libraries. The person who sets up the Shared Photo Library will be providing the iCloud storage to the entire library so the creator may want to look into iCloud+ depending on the combined size.

How to use iCloud Shared Photo Library - Apple Support

"When you contribute photos and videos to iCloud Shared Photo Library, they move out of your Personal Library and into the Shared Library. You can join one Shared Library, and you can choose what to share, or automatically share content straight from the camera. All participants have equal permissions to add, edit, and delete content in the Shared Library, while the person who set up the Shared Library, the library creator, provides iCloud storage for all of the content. Everyone else gets access to the Shared Library content without it counting towards their iCloud storage. 

When you join a Shared Library, iCloud captures a one-time snapshot of your photo library database and associated metadata and stores it for up to six months. This helps with a smooth transition of your content to Shared Photo Library. Any photos that were in your library at the time of the snapshot that are subsequently deleted are also stored in iCloud for up to six months. "

A much more limited option would be using Shared Albums.

How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support

I hope this helps.

When an iPhone and Mac are signed with same Apple ID and password on the same network and photos box is turned as on the photos will sync .

In Mac set up photo library and its preferences see the articles 

Set up and use iCloud Photos - Apple Supportsupport.apple.com › en-in

Change preferences in Photos on Mac - Apple Supportsupport.apple.com › en-in › guide › photos › mac

System Photo Library overview for Photos on Mac - Apple ...support.apple.com › guide › photos › mac

When photos are hundred percent synced , sign out Apple ID from an iPhone .

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV ...support.apple.com › en-in

And sign in with new Apple ID and password that is created with you in the past .

Sign in with your Apple ID - Apple Supportsupport.apple.com › en-in

Then share photos from Mac to iPhone .

Subscribe to shared albums in Photos on Mac - Apple Supportsupport.apple.com › en-in › guide › photos › mac

 The Apple ID and password are totally different in iphone and mac if you delete photos from mac or icloud the photos will be not deleted from iPhone .

The invitation has to be accepted to receive photos ( has to be subscribed ).

Share iPhone photos with Shared Albums in iCloud - Apple ...support.apple.com › en-in › guide › iphone › ios

Note : separate iCloud accounts will definitely be signed as different Apple ID its password with their own account credentials in different devices .