Yes you are correct - the Tableau Creator license includes Tableau Desktop. No functional difference.
The different licenses you would purchase for the other end users would really depend on what you need - do they just need to view & interact with dashboards or do they need to be enabled to do some self service analytics. Your Tableau Program Manager would be best placed to help answer this.
In the meantime the links below should help explain these new offerings...
Hope this helps
So I spoke to my program manager and got this cleared.
-The license we purchased contains tableau desktop only. It does not include server function.
-Creator contains desktop+server+prep, which allow you to connect to tableau server.
-I cannot transfer my desktop scheme to creator scheme.
-Desktop+Explorer does not work. Creator is needed.
So the key is tableau server, which is missing in my current set up.
Thanks for the update Xu, glad to hear its resolved now