Yes, there is a difference...unless it specifically says it's a whole grain bread, then it's basically just an enriched wheat flour used (usually unbleached wheat flour, but still stripped of it's original nutrients then re-enriched), with nowhere near the nutritional content.
Although...personally, I question how many of the so-called "whole grain" breads now being thrust on the market actually are...reading the labels they're still using enriched flour, and my understanding is that if something is truly whole grain, enrichment should be superfluous and unnecessary.
The cardiologist who wrote the South Beach diet book writes a lot about the differences between the two from what I remember. He encourages a whole foods, whole grains approach to eating whenever possible.
My very favorite source for bread (which, sadly, is back in my hometown in VA) is the Great Harvest bread store where they grind their own grain on-site for the various breads they bake (and you can get free slices hot from the oven with thick slabs of butter - yum).
My next best favorite -- but available even less often to me, lol -- is my best friend's whole wheat or oatmeal breads...She belongs to a grain co-op and grinds her own grain at home. But I only get a loaf every couple of months from her unless I really turn on the guilt...or if I go back for a visit. Then I have to endure the strange looks from security while they X-ray my bread for the return flight, lol.