The foundation is the base of the structure that provides the support the building needs to keep from settling drastically in either direction. We are experienced in all types you see today.
Slab-on-grade is generally used in areas where the ground does not freeze, thought it can be adapted with insulation in order to prevent it from being affected by frost heaves if placed in an area where the ground does, in fact, freeze. The slab is a single layer of concrete that is several inches thick. Edges of the slab are poured thicker in order to form an integral footing. Reinforced rods are used in order to strengthen the thickened edges of the slab. Typically, there is a layer of gravel beneath the slab in order to improve drainage. A welded wire mesh is cast into the concrete in order to prevent and/or reduce the chance of cracking.
Deep foundations support the structure when it is in an area where the ground freezes. In this situation a footing is placed below the frost line and a foundation wall is placed atop the footing. The footing, obviously, is going to be wider than the wall providing extra support at the base of the foundation. The slab is then poured between the walls.