What are red stars in Super Mario World?

I just finished watching this Super Mario World TAS. One thing that baffled me is, what are red stars for? They never seem to be directly earned, but simply some "bonuses" for clearing particular exits.

Is it so, or is there more to it than that?

You have to break (touch) the rope at the level's exit to earn stars. The higher it is when you break it, the more stars you get — up to 50. Getting all 50 gets you three bonus extra lives.

The white horizontal bar between the two vertical striped bars is the 'rope' to which I refer.

Once you have acquired 100 red stars, you enter a bonus game where you can earn extra lives.

The minigame starts with 8 squares that had changing icons on them (the one in center does not change). The 8 squares around the center rotate around the middle square. The objective is to hit the moving squares to make them stop changing their icons. Once you are done, you get an extra life for every row of similar icons.