The type of foundations you describe are called shallow spread footings. That is usually up to about 3m in depth.

The other class of foundation would be deep foundation, and that has several types.

Shallow spread footings: where surface soils have sufficient load bearing capacity and stability, concrete pads, strips, or rafts, are used to spread the forces from the superstructure over the ground, just deep enough to avoid unstable topsoil, frost penetration and seasonal moisture variations.
www.buildingconservation.com/articles/underp/underp.htm

Shallow Foundations
www.sampatti.com/did_you_know/shallow_found.shtml

I your case, you could call the pad foundation "simple", but that is not a classification, just an adjective.
Slab/mat/raft foundation is solid, and it is a frequently used adjective, "solid slab foundation", but again, it is a description.

What is the purpose of "classification" in this case?

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Note added at 5 hrs (2006-08-19 20:01:31 GMT)
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A chimney would only have "single" foundation if it was free-standing: would not be attached to any other structure (a wall for example). That is relaively rare. Industrial chimneys often stand alone, but these wouldn't have shallow footings.

Combined foundations are a mixture. When there are columns and walls within a building, they may need pads and strip foundation rrespectively, and this would be called combined foundation.