Notes and iCloud

I had the assumption that notes would automatically be backed up to iCloud with the correct settings in place. But what I have discovered is that I have different Notes on my iPhone and Notes in iCloud. Obviously I want my notes backed up, but I don't want two different accounts on my iPhone.

So am I correct in assuming that I should make all my notes setup for iCloud, to get what I want? So them I also have to copy all my notes that are only "On My iPhone" and paste them to the "iCloud" account in notes?