First part is a different set of post-processing techniques, second part is TruForm (though it turns out that may not be that useful after all unless I figure a way to get TruForm working on newer ATI cards).
Look at the angular parts in the picture to see the difference, the first picture has no anti-aliasing, so look at the bottom of the windows in the top middle, top of the stairs in the middle, and the 'bridge' in the top-left and you'll see the antialiased sections look a lot smoother.
Quincunx and 4xAA are basically the same thing, but Quincunx uses a + shaped pattern (the dot in the middle is modified by the squares next to it at each side and above and below) and the 4xAA standard method uses an X shaped pattern (the dot in the middle is modified by the squares next to it as well, but on its diagonal corners).
Which is which is noted in text above the pictures.