Switching Templates - and keeping content

I'm using Bedford at the moment, and would like to switch to Hayden. - when I switch templates I get the demo content for Hayden, not the content I developed in Bedford. If I switch back my content is intact in Bedford.

Am I missing something? I thought the content would be reflected in the new template?

If you switch templates, the new template will populate with the demo pages in case you want to use them, and the pages you've built in your current template will be moved to the Not Linked section in your Pages panel. This is because the navigation options above Not Linked are not the same on all templates. You can drag them up from Not Linked into your new navigation options once you've loaded the new template.

Thank you!