How can I tell the difference between newsletters in Hide from archive and Public?

Answer: 
Hide from archive and Public newsletters are both published and sent to the preferred audience. 

The only difference is that Hide from archive newsletter are not visible on the Archive page, while Public newsletters are. 

If the user/administrator wants to remove the Published newsletter on the Archive page, click the toggle switch to change the visibility. 

Below is an example of a newsletter that is on a Hide from archive status, and you can see this icon published 3 next to the Title of the newsletter.