For Lightroom on iOS/Android, and the web and desktop (not classic) versions of Lightroom, the cloud is primary storage, and the Lightroom apps on all devices are basically terminals that connect to and cache from that. So any photos you add to Lightroom on iPad are uploaded to Lightroom Photos in the cloud as quickly as the available Internet connection allows. After they finish safely being uploaded, they may be purged from the iPad cache especially when space gets low. If you edit any, those are downloaded back into the local cache on the iPad until you are done. All edits are always uploaded to cloud primary storage whenever an Internet connection is available. There is no “catalog” in the Lightroom Classic sense, because even the local edit data on the iPad is synced up to and cached from the primary storage in the cloud.
iPad storage may get low if many photos are imported and the available Internet conection cannot upload all of them to cloud storage faster than new images are added.
Now, the picture changes a little if you want to hook all this up to Lightroom Classic. You can sync one, and only one, Lightroom Classic catalog to your account’s Lightroom cloud storage. When you enable syncing from one Lightroom Classic catalog, and it connects to the cloud storage, it downloads everything it finds up there that is not already downloaded. This is because Classic wants to store all originals locally.
Lightroom Classic downloads all cloud originals to the designated Lightroom Classic sync download location (Peeferences / Lightroom Classic / Sync Location). It may be simplest to set this to the same location you use in the Import dialog box. This way, all images imported from anywhere end up in the same set of folders. After Lightroom Classic cloud originals, because they are now stored locally you can now back them up to other local storage.
Edits you make anywhere in the Lightroom system sync to anything else signed into that system. iPad edits will sync back to the Lightroom Classic catalog, edits to the same images in Lightroom Classic will sync back up to the cloud where the iPad can pick them up. There are a few exceptions, such as keywords.
For images in the Lightroom Classic catalog, only collections marked for syncing are uploaded, and only Smart Previews (not original files) are uploaded for editing on other devices. For Lightroom Classic, local storage (not cloud) is primary storage.
That’s a lot, but it summarizes how everything works. If you need more detail on each subject, a resource other than Adobe Help is the Lightroom Queen website. She has written detailed ebooks on both the cloud and Classic versions of Lightroom, although not everything might have a diagram.