Confused. Need help!

Hello !
I just created a new staging site.
When I click on button “Open” in section “Your Staging Sites:” (see screenshot 1) it is redirect me to the staging site. So everything work! But I confused in something: I am still staying on the same WordPress dashboard ,appearance of dashboard is not changed,I assumed it should change at least color. So I mean, if I will do any changes from WordPress dashboard,how I can define that these changes would apply exactly to Staging Site ?? And in same time how I can make changes to apply these changes to live web site,if dashboard looks same like before ?

Please explain me how it is work.