A structure need a foundation that supports it. If the structure is built on a soil that has bearing capacity which can withstand the weight of the whole structure, then you can design the foundation on footings alone. But if the soil is WEAK, you need piles to penetrate further the soil to have greater bearing strength.
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I think it is if its stiff against the wall or not. (Moment) I beleeve you are drawing in Revit?
The footing lies on the ground around the base of the structure. The Foundation cn go way below with pilings deep into the ground.I can say that the footing is the part of foundation which transfers the load directly to the soil and foundationis the part of structure below the plinth level including the footing while footing is the part which is below the ground level.
A or the footing is at the base of the foundation. Usually but not always 3 times the width of the wall. This just make a base for the wall to sit on so that it doesn't push into the ground. Without it, the wall would act as a knife and with the weight of the structure, cut into the ground.
A Piling mat is the base or road way which the piling rig will travel on. the design of the piling mat is required to resist the forces from the piling rig during travelling and piling. A piling matt should be constructed of suitable inert material (i.e. not tennis balls).
Isolated footing Transfers individual column loads directly to the soil. If a single spread footing interferes with another spread footing, the two can be combined to form a combined footing.