iphone Storage issue, un-used iCloud storage

I am constantly getting alerts on my iphone telling me that I don't have enough storage despite having 34.73GB of iCloud storage available. The biggest issue is photos eating up space. I thought that if you have sync'd to the cloud, the storage is then in the cloud not on the phone, but that doesn't appear to be the case. Plus if I look to delete a photo off of the phone that is already in the icloud, it says it will delete it from both places, so that's not an option. Surely it can't be the case that a photo is stored both on the phone and in the icloud, otherwise what is the point of icloud? I must be missing something in a setting somewhere, but I just don't know where. Any advise?