Hey there, Huelyn!
Thanks so much for using Apple Support Communities.
Congratulations on the new iPhone! That is always a fun experience and we'd hate to think that your storage issues could put a damper on that. We think we can help shed some light on this.
Your device has two types of storage to note; on-device and iCloud.
Your on-device storage (the 64GB) includes your system data and things like the apps you install. iCloud storage, on the other hand, would be things like your backed up data and your photos and videos that are stored in the cloud. This can get tricky if you're seeing a pop up message but you're not sure which data type is affected.
Here is some more information that we believe will help: What's the difference between device storage and iCloud storage?
Can you give that article a read-through and let us know if it helps?
We hope this does the trick for you!
Cheers.