I can't find bread flour!
It's the amount of protein (gluten). Bread flour has a higher percentage. You could use whole wheat flour and add wheat gluten.
Bread flour as you buy in the store is usually white flour made either with wheat which has a naturally higher gluten (protein) content than all-purpose flour, or is flour with added gluten. Whether or not a flour is specifically bread flour has to do only with the amount of gluten and not whether it's white or whole wheat. If you can't find bread flour, adding gluten to all-purpose flour or a whole wheat flour will work. It's also important that hard red wheats (either spring or winter) will have more gluten than soft red or white wheats and are better for making bread.
I disagree with the above answer. The biggest difference between the two is that bread flour is a white flour made only of the endosperm and whole wheat includes the germ and bran. The closest flour to bread flour would be regular unbleached white flour. Bread flour does have a slightly higher protein content than regular white flour but the folks at King Arthur Flour say it can be substituted without harm.
Hope Preston is correct about the contents of whole wheat flour. It actually has a significantly higher protein content than bread flour. Bread flour's protein, or gluten, content is 12-12.5%, while that of whole wheat flour is 14-14.5%, equal to that of high gluten flour which is used to make bagels. That's a difference of 17%, which I think is significant. The reason for whole wheat flour containing more protein is to compensate for the scissoring action that can result from the sharp edges of the bran. During the kneading process, it tends to literally cut, or shorten protein strands. And since protein is what literally holds bread up, well, I imagine you're getting my drift. Bread flour can mean many things to many producers. Look for any flour labeled "best for bread," or even "good for bread machines." If the work bread is mentioned anywhere on the label, you can trust that it is bread flour.
Giovanni50, I just sent you an email with a bit more information about true bread flour, and a link to a site which rounds it all out for you. Happy baking.