So, I'm new to Mac. I used Windows during my career (retired now). I know that clicking the red dot x does not quit the program/app. I thought I was okay pressing the red dot x, followed by pressing on the icon in the tray, and choosing Quit from the menu that shows up over the icon.
For some reason (or no reason?) pressing command Q to quit Safari is different from what I mentioned above. If I press command Q to quit, then when I open Safari - sure enough, my previous session is restored!
So I will always use command Q to quit Safari.
Thanks again for your help, @dialabrain (cool name, BTW).