A bun is a kind of bread. Bread is the basic word for food made of flour, water, yeast etc. There are sweet breads, but in most cases bread is the umbrella term for many types, such as buns (e.g. hamburger buns), baguettes, loaves of sandwich bread, focaccia, etc. etc. etc. Buns are generally somewhat round, light, and good for making sandwiches of some kind, or else they are sweet buns, like a light donut (but not in the shape of a donut!)

A bun is a round lump of dough, as Eric says, like a hamburger bun. Bread is also dough made or bought in a loaf which can be cut into slices.

A bun can be 2 things but both are types of bread and round shaped: 1. The plain round bread used for burgers. 2. A sweet bread, sometimes with sugar icing on top or a filling inside. I hope this helps :)