Whole wheat - means the bread was made with the whole wheat grain, but make sure it says 100% whole wheat, or read the label to make sure it ONLY contains whole wheat (and not a combination of whole wheat flour and wheat flour, which is flour made from wheat with the bran layer removed).
Whole grain, means it's made with the "whole" grain (with the bran layer), but it may be any or a mixture of grains. Again, read the label carefully to makesure it says 100% whole grain, and not "made with whole grain," which just means whole grains were added, but there may be refined flour also - read the ingredient list.
Multigrain - just means a variety of grains were used, perhaps whole grains, but also perhaps refined grains (grains with the bran layer removed - and with it a great deal of fiber). Again, read the ingredients to see whether only whole grains were used, or a combination of whole and refined.
Probably the best bread overall would be one that was made with only whole food ingredients, several grains, but only whole grains (no white flour, but sometimes white flour is listed as "enriched wheat flour," or only as "wheat flour.")