Happy to provide some more information.
Notifications are indeed used for moderator messages specifically. If at any time a moderator takes action on comments or discussions you have created you will receive a message with the details of why.
My Updates are for activity around your comments/discussions. Example: I comment on your discussion here and you will receive an update in 'My Updates' letting you know what I've said and allowing you to jump to this thread easily.
Let me know if you have any other questions.