Explain iCloud Photos VS Photos in iCloud Backups

So I recently just got iCloud+ for $2.99 to backup my data before I did a reset on my phone. At first, it only showed Photos taking about 108gb on my iCloud and I had 91gb of free space left. Then when I went to check my iPhone Storage, it went down from 124gb to a whopping 34gb after syncing to the cloud.

But after backing up my data before reset, I noticed it included my photos (that were already backed up to the cloud) in iCloud Backup and now it’s almost full at 199/200gb!!! And now I see my iPhone storage being at 117.82/128gb. It wasn’t like that before the reset, what’s going on???

I’m so confused. How do I make space on my iCloud+ and on my iPhone Storage without compromising everything I have on my phone and account?

Will deleting photo library from iCloud Backups erase everything from my iCloud Photos as well?

Or will I still have access to all of my pictures even after deleting them from iCloud Backups? Do either of them affect the other?

Ex: Deleting iCloud Photos will permanently remove them from iCloud Backups, OR, deleting iCloud Backups will permanently delete everything from iCloud Photos as well.

An extremely detailed explanation would be very helpful and greatly appreciated since I’m not understanding any of this right now, thank you!