A full adder circuit has three inputs (A, B, C) that add the input numbers and generate a carry and sum output. It is different from a half adder which only has two inputs and outputs. A full subtractor circuit performs subtraction on three input bits: minuend, subtrahend, and borrow in to generate a difference and borrow out output. Both circuits can be implemented using universal gates and have applications in arithmetic logic units, ripple carry adders, multiplication circuits, and other applications requiring complex computations like graphics processing.