S21 is the forward voltage gain of a two port network when the input and output ports are matched to the system characteristic impedance. S11 is the input reflection coefficient. S22 is the output reflection coefficient . S12 is the reverse voltage gain. If the device is a linear passive network it will be symmetrical so that S21=S12. If it is an amplifier or some other directional device then the two gain figures are definitely different.
There is no global x2 factor in the definition of S21. It could be that any particular setup requires a x2 factor as a scaling because of an attenuator or some such thing.
