Why are there different pasta shapes?
Some of it is culinary: different sauces adhere better to different shapes. So fettucine is better suited to an alfredo sauce, etc. etc. And some of it is purely aesthetic: new shapes created solely for the way they look. Alton Brown did a great breakdown on the pasta episode of Good Eats (here’s a transcript; scroll down to Scene 4).
The Cook’s Thesaurus (which is a fantastic resource) has a page that identifies different pasta shapes, and what sort of sauces/preparations work best with them.
The functionality is largely secondary to the product differentiation aspect. The medieval Italians went nuts for pasta and pasta makers developed literally hundreds of variations trying to outdo one another. Some are regional, some are symbolic, some are indeed predominantly functional, but there are something like 860 “official” pasta shapes and not all of them have specific uses.