Why do I receive Software Update notifications if there are no updates available?

If you run the new 'Ubuntu Software' application (same icon as the old 'Ubuntu Software Centre', i.e. a capital 'A') the you will see the updates. I'm not sure why 'Software Updater' (icon is a circle with arrows) is out of sync but it is. I asked a related question here

The extra and outdated notification messages are a bug. This has been fixed in development and the update will be released for Ubuntu 16.04 soon, probably later this month (June 2016).