Notes - iCloud.com vs me.com
As @Tetsujin said, iCloud.com, me.com and mac.com are all the same, the latter two are alias' of iCloud.

In Notes on the mac select View > Show Folders. You should now see where your notes are being saved and will have a heading for "iCloud" and "On my Mac". If you don't see "On my Mac". Select from the menubar Notes > Preferences and check the box "Enable the On My Mac Account".

You can now drag notes from the list in the middle to the groups on the left.