Seems to now be no way to add more information to this post.
I have also noticed that either the app or something in the syncing randomly changes data, so I will go to a note, and see it has changed on the desktop app, then see the same change has been applied to the mobile app (or vice versa), which I have not done myself. Very frustrating!!!
Mac Studio, macOS 14.4
Where were the Notes? See the pic below. You will get your answer
The various options that you are referring ("the second text menue") to will exist only if your Notes are on iCloud or the "On My Phone" Folder.
The 2 pics below are self-explanatory.
If you're missing notes on your iPhone, iPad, or iPod touch
Notes are always synced through Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other email Account
Any data on your device that isn't synced regularly will be stored in your iCloud Backup. With Backup turned on, iCloud takes periodic snapshots of this data to make sure it's easy to restore any time you get a new device. Between syncing and backing up, all of your data is kept safe in the cloud.
What does iCloud back up? - Apple Support (IN)
Thanks for responding SravanKrA. I only sync my notes through iCloud- see below.
I am not sure what the top item, Shared means- I have not noticed it before, and it only is referring to one of my notes, but all of them are syncing with the phone, so...
On the phone, they are syncing through iCloud as well.
Thanks.
Issues with Notes app on iPhone- searches, cursor moving, font sizes/colors not displaying properly
