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.