About the shallow foundation and deep foundation we can speak a lot. Different site conditions and types of building requirements need different foundation.  Foundation connects/interfaces two different materials, their strength ratios are of the order of several hundreds. As a result, the load may be spread to the soil in a manner such that its limiting strength is not exceeded and the resulting deflections are tolerable. 
From design point of view, shallow foundations are classified as:
Wall footing
Isolated column footing or pad footing
Combined footing
Cantilever or strap footing
Mat foundation

Deep foundations examples:- Pile foundations, pier foundations and wells or caissons foundations.
The images will show you more about the types of foundation and the links will explain it better.

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