Loaf, sourdough, and pumpernickel are types of bread. A rye is not a bread type.
Loaf - Bread that is shaped and baked in one piece and usually sliced before being eaten.
Pumpernickel - Dark, dense German bread made from coarsely ground whole-grain rye.
Sourdough - Leaven for making bread, consisting of fermenting dough, typically that left over from a previous batch.
Rye - A wheatlike cereal plant that tolerates poor soils and low temperatures.