iCloud is actually several services. There is no one place to go to see all of them.
iCloud Drive - Files stored by apps and the iPad. The Files app the best way to view them outside of the app that created or owns the file. Pictures stored in a third party app or using the Files app do not show up in the Photos app.
iCloud Photo Library - Stores photos in iCloud and allows didferent devices and computers to keep them synced.
iCloud Backups - Backup and restore from iCloud. All or nothing.
Syncing and storage for many Apple Apps: iBooks, Calendar, Contacts, Reminders, Notes, Pages, Numbers, Garage Band, etc. Some of these can be viewed in the Files app, many are only viewable from within the apps themselves.
Third party apps - can sync or store files in iCloud. Most of these can be accessed via the Files app, but not all.
More things I’m not remembering right now.
And you are right. The Mac OS works differently. Except where it syncs with iCloud and iOS devices.