For foundations that experience sinking there are several form of piers being used today.
Drilled Piers involve drilling a series of holes around the foundation down to the level of stable soil and then installing each pier using steel rebar and poured. The concrete requires seven days to set up, so the crew must return later to actually level the foundation. The jack up the house above each pier and stack pre-cast concrete blocks and steel shims between the pier and foundation until the foundation is level all around. With this method the weight is transferred from the house to the bottom of the pier.
Piles are more recent methods developed in the 1970's. They are underground support systems made up of a series of cylinders that measure six inches by 12 inches.
With concrete piles, the cylinders are hydraulically driven into the ground one on top of the other until they won't go any further. The foundation is leveled as soon as all piles have been driven. One type of concrete pile uses solid cylinders that are simply stacked vertically underground. The other types use cylinders that have hole in their centers. Either cable or rebar is run through the holes, thereby improving lateral support and alignment.
With steel piles, sections of pipe are pushed into the ground with the same method. The steel pipe is narrower, about 3 inches in diameter, than concrete, which is about 6 inches. This means it take less force to push the pipe into the ground and it also goes deeper than concrete.
On both of these methods, the weight of the house is transferred from the surface to the sides of the piles. It holds the weight of the structure because the soil grabs hold of the pier. This means it has a lot more longevity than drilled piers. This is why the warranties are longer.