They are just different ways of counting the points.
I can't quite remember all the details so if anyone else knows more please feel to correct me
I believe the 123 & winning points programs gave you a daily point allotment (maximum you could eat) and you had to save up points by keeping track of any unused points for the week and by accumulating points through exercise. You could then spend these saved up points on food but once the week was up you started fresh the following week.
With flexpoints you have a minimum amount of points to eat per day and you can get extra points through exercise. You are also given 35 points per week on top of that minimum daily requirement to spend as you see fit. When that week is up any points you have not spent are gone and you start fresh the following week.
The core program does not count points per day but you are restricted to eating the foods on the core food list. You also get the 35 flexpoints which you use if you eat something that is not on the core food list.
Also there is now more of an emphasis on eating better carbs (whole grain/wheat) brown rice etc, and on exercise than there used to be on the old programs.
I honestly can't remember what Quickstart was so if any one else knows and can post about it that would be great.