Norton Internet Security Product Update Questions

My Norton Internet Security recently had an update, I received a notification saying to restart to install and my icon is now a yellow circle with a check mark. Previously it was a grey box. It still says Norton Internet Security but is there a difference in this new program update besides just the appearance of it?

My dad has Norton Security and it looks exactly the same. 

Is this new version of Norton Internet Security still different than Norton Security or is it still called Norton Internet Security on my computer since that is what I already had? Is there still a difference between Norton Security and Norton Internet Security?

 

Also, right after I restarted to finish installing there was a red x and it said that the firewall was turned off even though I never turned it off. I fixed it right away when the notification popped up to fix now which was a few minutes after I started up my computer, but what are the chances I could have gotten a virus or malware during that time?