To start off with we need to explain that Preferment is any bread making technique that combines a moderate percentage of flour with a tiny amount of leavening and a small amount water and lets it develop for a period of time, anywhere from an 1 hour to a week or two, unlike a sourdough start that can be kept active for years. Biga and poolish are both types of this preferment and they can both be made from another type of flour than the one you are using for the actual bread. For example, you can use spelt, rye or whole wheat flour to add different flavours to our bread.
Biga ---- (Italian) is generally lower hydration at about 60 to 70 percent hydration, which make it a firmer start. The main function of a Biga is to enhance the strength of the dough, but also has a positive influence of coaxing the flavor out of the starches of a well maintained start and is often used in those breads that need a light, open texture with holes. Many of these breads include the popular Italian breads, such as ciabatta or pane all'olio. Biga also helps to preserve the bread by making it less perishable.
Poolish ---- (Polish/Austrian) is generally 100 percent hydration which creates a very soupy start. Usually a poolish is fermented at room temperature and the amount of yeast used depends on the time you want to ferment the poolish, meaning less yeast needs more time. You get a richer flavour due to increased acidicity and you gain a longer shelf life.
Sponge ---- (English) is like a poolish but contains all of the water and is quite thin and runny
Pate Fermentee ---- (French) is also considered a firmer start, but greatly differs from the Biga. It is usually purpose-made and includes salt. It is kneaded a bit then put in the fridge overnight or for a few days.