That was a question on my mind: supposedly there are ~400billion stars in our galaxy. So, does the game have ~400billion stars, or ~400billion systems (in which there will be way more than 400billion stars because some systems have many stars).
However, all dots you see in the galaxy map are visitable if 1) you can get there 2) if you have a permit for the system if it is required. There are at least 5 known regions of space on the far side of the galaxy that, for some reason, you cannot get into. It has been theorized that those regions are set up for future expansion of the game.
Good luck and Happy Hunting!
//Pappy