Like wood, metal has a grain structure. Metal that is pounded into shape in a forging die ends up with a grain structure that is formed around the external shape of the object, so you don't have "endgrain" on all the corners. This gives a shaped forging superior strength and resistance to cracks, and therefore these parts will be rated the strongest.
A "billet" is a chunk of forged aluminum, so it was exposed to forming stresses just like a shaped forging. The difference is that there is a lot of exposed "endgrain" when the final product is machined from the billet block. While the part is still technically forged, it is less strong than a shape-forged part due to the grain structure of the metal.
An extrusion (metal "squirted" out of a forming die into a "stick") will often have a tigher grain structure on the outside (similar to a forging), but a looser, weaker grain structure in the middle. This may or may not matter, depending on what final machining you do, but generally, an extrusion is considered not as strong as a shaped forging or a part machined from billet.
Finally, there are castings, which is literally liquified metal poured into a mold. These will be the weakest by far, as aluminum in particular makes for relatively poor castings. The grain structure is very open in a casting, and voids (tiny pockets of air) will be present throughout. Castings are particularly vulnerable to impacts or other sudden changes in pressure, which tend to make a casting shatter. Cast AR parts are typically made thicker than a similar forging to help make up for the weaker properties of the metal. Member Tweak has reported that it was common for cast AR uppers and lowers to shatter during their machining processes (yes, they still require some machining) when he worked at Olympic Arms. And virtually all of the broken lowers ever posted on AR15.com have been cast lowers.
-Troy