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Mat foundation is a foundation designed for a structure with heavy loads because of close column distribution, also for a soil that can sustain a load that shall make (isolated) footings overlap, and in the case of underground water (UGW) fluctuated level that might seep through the isolated footings into the basement. Thickness of the mat shall depend on these factors associated with each case.
Design shall take into consideration (edge) column, (intermediate) column and (corner) column as separate cases. Additional rebars must associate larger positive (Upward) moment at the top of the column peripheral area, and the larger (Negative) moment that occurs at the mid-span between columns. What you are calling a (beam) foundation makes me understand you mean (Strip) footing that carries a line of columns at a time. If I am right, then strip footing is used for other cases where mat and isolated footings are not economical or feasible, soil allows no overlapping of parallel beams, and UGW is irrelevant (No basement involved).
