The basic idea is this:
If it supports in game saving, then it does in game saving. Example: Mario 64. If I get a star, when I save in the game, it's just like the N64 cart. So if I go from 8-12 stars and quit the game after saving, and then load it up again, it goes to the regular menu/profile screen, and I can choose profile 1, which has 12 stars. The other profiles retain their own information.
If it's a game like Zelda [NES], it's kind of like save stating, but not as deliberate. I.e., looks like I can save at certain points by using the Home button to close out of the game. I think these are arbitrarily determined by Nintendo, and would function in ways you might imagine. I.e., in Zelda [NES], the last door you went through (this tends to be a dungeon for me). In Kid Icarus, it's the beginning of the last level you quit/died out of.
Correct me if I'm wrong. I think someone already said basically this in this thread anyway.