It is correct that iCloud Storage and iPhone Storage are not the same.
iCloud is a Backup option for your photos, videos, contacts, calendars, etc. If you have, for example, 5GB of photos in your Photo app on your iPhone, then the 5GB photos will synchronize with iCloud, and your photos will also take up 5GB in your iCloud. But the pictures still take up 5GB of your iPhone's internal storage space. iCloud is therefore not an additional storage space for one's iPhone's storage space.
When you make an iCloud Backup, the backup will contain everything that is not already synchronized in iCloud. An iCloud Backup does not contain your photos as they are already in iCloud.
You can see how much space you have available in iCloud here:
Settings → Apple ID → iCloud. There you can also see which services are enabled to synchronize with iCloud. I would recommend having all services activated.
If you make an iCloud Backup and there is not enough space for it in iCloud, you can upgrade to iCloud+ and thus buy more space for your backups. Read more about iCloud+ here.
You can read about the difference between iPhone Storage and iCloud Storage here:
What's the difference between device storage and iCloud storage? - Apple Support
You can see what an iCloud Backup contains:
What does iCloud back up? - Apple Support