This post from a blog called alansmysteriousworld.wordpress.com rises to the top of Google's hits when one asks "difference between bun and roll."
I think its finding that (in the U.S., at least), "The US Food and Drug Administration ... draws no distinction between buns and rolls" may be the most significant finding.
What’s the Difference Between a Bun and a Roll?
September 17, 2010
The US Food and Drug Administration stipulates only that breads weigh more than one-half pound per unit and that rolls and buns weigh less than one-half pound. All three starches must be yeast-leavened bakery product. But the FDA draws no distinction between buns and rolls. And neither do retail bakeries. One company’s “hamburger buns” is another’s “hamburger rolls.”
Tom Lehmann, a trusty source at the American Institute of Baking, while conceding that there is no clear-cut answer, passed along a short write-up that the Institute prepared: “The term ‘roll’ is generally applied to filled products, especially those that are formed by sheeting and rolling-up or folding the dough, such as cinnamon rolls (which, in many areas, are sold as cinnamon buns) and Danish rolls. There are exceptions to this, however, in that hard-crusted products are also included in the roll category. Products of this type include Kaiser-rolls and French rolls. Buns, on the other hand, are generally more bread-like in shape (round or elongated) and typically do not contain a filling. The one notable exception to this is the Easter favorite, hot-cross buns.”
Simon Jackel, director of Plymouth Technical Services, concurs with the Institute, but argues that it might be more accurate to contrast them by indicating that buns are usually soft, and that rolls can be hard or soft. But ultimately, Jackel muses that pinpointing the answer to this question is “sort of like asking: ‘Is it a hamburger or a chopped-beef patty?’”
(Submitted by Robert Lawler of Ivyland, Pennsylvania)