On my Mac, is Norton running?

Hi community. On the menu bar at the top of the screen on my Mac I can see the Norton symbol (a tick inside a circle). Does this tell me that Norton is running? When I click on it the drop down menu tells me "Safe" with a green tick. Do I also need to launch Norton security and have the Norton window open to be protected? The window I am referring to shows "Security", "Scans", "LiveUpdate" etc. This window opens automatically when my Mac starts up and tells me that I am protected. Can I close this window and still be protected? Thanks for your assistance.