I am using Windows 10 on both PCs. My photos are saved in OneDrive.
Then, the OneDrive service does automatically 'sync' to the Cloud all the files (pictures or documents) stored in the dedicated OneDrive folder; and the service allows you to sync from the Cloud to another computer and reciprocally. If you update or add pictures in the OneDrive folder, that will sync with the other computer. For more details, search in the OneDrive help.
However, that does not work for the catalog. There is no easy solution to share a catalog and in my opinion it would not be a good idea to store the catalog in the OneDrive folder. Working in the organizer while the 'syncing' is taking place may lead to unexpected results and anyway, the catalog would only point to the drive in the original computer. All photos would be seen as disconnected on the 'synced' computer.