Okay, I may have been living under a rock but Apple changed the way it is doing notes when it came out with IOS 9. I never noticed the difference on our devices because they had been syncing in the past and very little had changed on either side. Once we got a new device it became very obvious that syncing was not working.
All notes that were created before IOS 9, were created in a local folder on the device. When IOS9 came out they added a new folder called iCloud Notes. The notes from the local folder are not being synced any more.
Apple did not make an easy way to copy over the notes from the local directory to the iCloud directory.
There are two ways to fix this problem.
1. Send each note to yourself in an email. Then create a new note and do a copy/paste into it. Once that is complete you can edit a note and select it with the check mark. At the bottom, a Move To shows up and you can move the note to iCloud Notes. It will now sync assuming you have the correct email account set (xxxx@icloud.com) and that notes are being synced on both devices to iCloud.
2. You can do a similar thing by using airdrop. It saves you the email.
Once you are done doing the copying, this arrangement does make sense. There are notes such as shopping lists and such that I only want on my phone. There are other files that I would always use on an iPad but
never want on my phone. There are some files that I would want in both places. This allows the user to choose what stays local and what gets synced.
This took me way to long to figure out because I thought there was a setting that was wrong some where.
It never occurred to me that it was a change made by Apple.