Hi Craig,
Thanks for the questions on this. Just to be clear Optimized Routes and Shared Routes are two different but related concepts.
An Optimized Route is really just a multi-stop route which has been optimized such that the ordering of the stops in the route are sequenced in the optimal order. At the 2.0 release of Navigator (which will be released in the coming weeks) there is an option to generate route optimized in this manner. This is a new feature at the 2.0 release of Navigator.
Shared Routes is a broader concept that one will be able to use many of the great tools we have on the ArcGIS Platform for creating routes and sharing these routes with drivers in the field who are using the Navigator App. This is still being designed and probably won't be available until later in the year.
The "Save" button in the Directions Widget which is part of the ArcGIS Online Map Viewer is merely a way for users who are already using this functionality to save the result of directions generated by the directions widget. Currently Navigator has no way of consuming these saved directions. Moving forward there will be one unified experience to generate, save and share routes in the platform with Navigator being the logical app to consume these routes in the field. The Umbrella term we are using for this, at the moment, is "Shared Routes".
Hope this helps clear things up and thanks again for the feedback.
-Brent